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J22 """' 3" 33.33331"- 131333323222-223’233‘323‘31222222... ..2.2?.3.'322:2.3.~'.‘- THESlS Q.” / ESR SITY LIB BIHAR ES Illllllllllllllllllllllllllll Ill ll ill I 3 1293 01565 ll LIBRARY Michigan State 1 University This is to certify that the thesis entitled Accuracy Assessment of a Mobil Video Platform used for Kinematic Analysis of Rowing presented by Matthew Joseph Weise has been accepted towards fulfillment of the requirements for M.S. _degree in Physical Education and Exercise Science QMQW / Major professor / Date Jé'nkflC/ 2,2 /?97 0-7539 MS U is an Affirmative Action/Equal Opportunity Institution PLACE ll RETURN BOX to roman this checkout from your record. TO AVOID FINES Mum on or bdoro dot. duo. DATE DUE DATE DUE DATE DUE l l | I MSU In An Affirmative Action/Equal Opportunity Institution m m1 ACCURACY ASSESSMENT OF A MOBILE VIDEO PLATFORM USED FOR KINEMATIC ANALYSIS OF ROWING By Matthew Joseph Weise A THESIS Submitted to Michigan State University in partial fullfillment of the requirements for the degree of MASTER OF SCIENCE Department Of Physical Education and Exercise Science 1997 ABSTRACT ACCURACY ASSESSMENT OF A MOBILE VIDEO PLATFORM USED FOR KINEMATIC ANALYSIS OF ROWING By Matthew Joseph Weise A Mobile Video Platform(MVP) was developed to study three dimensional kinematics of rowing. The MVP holds two cameras and is towed by the rowing shell. Systematic errors occur in digitized data obtained from video images of the MVP due to movement of the cameras relative to the field of view. The effect of camera movements on calculated spacial coordinates were examined by testing the change in known spacial coordinates when systematic changes occurred along the x, y and z axes and in the xz, yz and xy planes. It was concluded that the MVP’s present design is not a valid technique for studying the kinematics of rowing. However, by mounting the cameras to the shell the uncertainty decreases substantially, especially in x-coordinate data. Mounting the cameras as well as increasing the angle between cameras and the field of will yield a valuable tool in studying the kinematics of rowing. To my wife, Lisa. Thank you for your patience, support and motivation through this endeavor. ACKNOWLEDGEMENTS I would like to thank Karl Pearson for constructing of the Mobile Video Platform and aid in data collection. Also, thank you to Dr. Eugene Brown, Dr. Simon Billinge and Dr. James Pivarnik for their advice and guidance in this experiment. TABLE OF CONTENTS LIST OF TABLES ........................................................................................................ x LIST OF FIGURES ...................................................................................................... xi LIST OF ABBREVIATIONS AND SYMBOLS .......................................................... xiv CHAPTER 1 Ingodoction ........................................................................................................ 1 Lugoog ..................................................................................................... 3 Hymthgis ................................................................................................ 3 Defmit_ion of Terms .................................................................................. 3 Assmotion .............................................................................................. 6 CHAPTER 2 Litogture Review ............................................................................................. 8 Two Dimensional Cinematography .......................................................... 8 Thr imensi n M of An sis ................................................ 10 Rowing Meohogics ................................................................................. 12 CHAPTER 3 m ............................................................................................................ 13 The Mobile Vidoo Plgfi’orm .................................................................... 13 mm ............................................................................................. 17 Viogtaoing MVP Movomont Whon In Tow .......................................... l8 Calibration Frame ...................................................................... l8 Mgkers ...................................................................................... 19 Videotaoing and Digitizing ......................................................... 20 Calculation Of MVP Movements ................................................. 22 Treatment of the Movements of the MVP ............................................... 24 Esfiblishing Control Coordinates ............................................................ 25 Calibration Frame ....................................................................... 25 Esmlishing Uncertaing of the MVP ...................................................... 26 Moasygiog L Y, Z, 6, Sb. and .............................................................. 28 Tr e f L b r Da ........................................................... 31 CHAPTER 4 Mtg .............................................................................................................. 32 Effects of Rowing Cycle Events on MVP Movemgms ............................ 32 Maximum Movements of the MVP ......................................................... 39 Unoortgim Mwements ...................................................................... 40 n ' of MVP .......................................................................... 42 CHAPTER 5 Disgssion ......................................................................................................... 44 Red in Un e in Mo tin Cameras to the Shell ....................... 44 Disadvantages of o Camera System Agched Directly to 3 Shell ..................................................................................... 45 Advgggg of 5 Camera System Amhed Dirfly go a Shell ..................................................................................... 46 Estimated Error in Kinematic Qgculao'ons when Camerg Rotate in the YZ Plge .................................................. 46 Estimatfl Percent Error .......................................................................... 48 Further Testing on the Uncertainty Coefficient ......................................... 48 Conclusions ................................................................................................ 48 APPENDIXES A. Cmrdiriaies of Mobile Video Platform Ma_rk_er§ ............................................. 49 B. Calculations of x-axis Movements of the Mobile Video Platform .................. 59 C. Calculations of Itaxis Movements of the Mobile Video liatfonn ................... 66 D. Calculations of z-aéis Movements of the Mobile VideoPJlatfonn ................... 73 E. Calculations of xz Plgie Movements of the Mobile Video 80 Platform ......... 8O F. Calculations of vz Plane Movements of the Mobile VideoLlatform ............... 87 G. Calculations of Y2 Plane Movements of the Mobile Video Platform .............. 97 H. Calculations of xv 11am Movements of the Mobile Video Platform ............. 107 i,_'I_‘able of Movements of the Mobile Video Minn ..................................... 117 J. Digitizeo Coordinates, dn, and (In. / d Calculations of Point A .................. 120 K. Digitized Coordinates. d_n,~_ and dn, / dQ Calculations of Point B .................. 126 L. Digitized Coordinates, drI_-L and dn, / dQ calculations of Point C ................... 132 M. Digitized Coordinges, dn_-L_and drii / dQ calculations of Point D .................. 138 N. Digitized Coordinates, dn, and dn, / dQ calculations of Point E ................... 144 O. Digitized Coordinates, dn, and dn, / dQ calculations of Point F .................. 150 P. Digitized Coordinates, dn, and dn, / dQ calculations of Point G ................... 156 Q. Digitized Coordinates, dn, and dn, / dQ calculations of Point H .................. 162 LIST OF REFERENCES ................................................................................................. 168 vii LIST OF TABLES Table 3.1. dQ values for each Q ...................................................................................... 28 Table 4.1. Movements of the MVP from the digitized data ............................................ 39 Table 4.2 Range of values used in laboratory testing ...................................................... 40 Table 4.3. Average dn, / dQ ............................................................................................. 41 Table 4.4. Percent of total dn, / dQ .................................................................................. 42 Table 5.1. Calculation of the uncertainty in linear and angular acceleration given a rotation in the cameras of five degrees in the yz plane .................... 47 viii LIST OF FIGURES Figare 1.1a. Catch ............................................................................................................... 6 Figig 1.1b. Finish .............................................................................................................. 7 Figge 1.1c. Hands and upper body away ........................................................................... 7 Figu_re 2.1. The rowing motion as a first and second class lever ..... 12 Figu_re 3.1. Specialized hitch to allow the shell to pitch and roll ..................................... 14 Figare 3.2a. Three dimensional view of the MVP ............................................................ 15 Figge 3.2b. Top view sketch of the MVP ........................................................................ 15 F igar_e 3.3. Calibration frame with stakes ......................................................................... l9 Figu_Le 3.4. Five markers used to study the movement of the MVP .................................. 19 Figge 3.5. Top view sketch of the videotaping area ........................................................ 21 Figare 3.6a. Positive and negative MVP movements in the xz plane ............................... 24 Figge 3.6b. Diagram of variables used to solve for movements in the xz plane .............................................................................................. 24 Figu_re 3.7. Calibration frame and points treated as unknowns ........................................ 26 Figu_re 3.8. Positive and negative MVP movements in the yz plane ................................. 29 Figaro 3.9. Positivie and negative MVP movements in the xy plane ............................... 29 F igu_re 3.10a. The Floor Mounting Boards and the Camera Mounting Board as seen from the calibration frame ................................................................. 30 Figu_re 3.10b. Right half view of Camera Mounting Board and the Floor Mounting Board as the system is rotated in the yz plane ........................... 3O ix Figu_re 3.10c. Top view of right Camera Mounting Board and right Floor Mounting Board ......................................................................................... 31 ‘ Figare 4.1a. Movement of the MVP relative to the shell along the x-axis ....................... 33 Figu_re 4.1b. Movement of the MVP along the y-axis ....................................................... 34 Figaro 4.1c. Movement of the MVP relative to the shell along the z-axis ....................... 35 Figge 4.2a. Movement of the MVP relative to the shell in the xz plane ......................... 36 Figge 4.2b. Movement of the MVP in the yz plane ......................................................... 37 Figare 4.2 c. Movement of the MVP in the xy plane ........................................................ 38 Figare 5.1. Top view sketch of cameras attached directly to the shell ............................. 45 “I. LIST OF ABBREVIATIONS AND SYMBOLS Symbol Definition dX’ maximum change in the position of the cameras along the x-axis dY’ maximum change in the position of the cameras along the y-axis dZ’ maximum change in the position of the cameras the cameras along the z-axis dO’ maximum change in the position of the cameras the cameras along the xz plane when towed by the shell do’ maximum change in the position of the cameras along the yz plane d‘I” maximum change in the position of cameras along the xy plane partial derivative i digitized point A, B, C, D, E, F, G, or H n x, y, or z n, comm. control x, y, or z coordinate of the ith point Q X,Y, Z, 9,¢,or‘I’ dQ camera movement in X,Y, Z, 6, 4) , or ‘I’ U,( uncertainty in the digitized x coordinate Uv uncertainty in the digitized y coordinate UZ uncertainty in the digitized z coordinate x digitized x coordinate y digitized y coordinate z digitized z coordinate X change in position of the cameras along the x-axis Y change in position of the cameras along the y-axis Z change in position of the cameras along the z-axis Abbreviation Definition APAS Ariel Performance Analysis System CMB Camera Mounting Board FMB Floor Mounting Board MVP Mobile Video Platform Mix Svmbols ltfrtcam: lefi camera’s front marker libkcam: left camera’s back marker rtfrtcam: right camera’s front marker rtbkcam: right camera’s back marker shell: shell marker len: calculated length of the distance between the right camera’s front and back marker frame number CHAPTER 1 Introduction The sport of rowing consists of a repetitive motion that uses sequential muscular contractions to exert force on an oar to propel a shell through the water. A typical race covers a distance of 2000 meters, takes anywhere from five to eight minutes and requires each rower to take 250-3 00 strokes. These strokes are performed at a frequency of approximately 30-40 per minute. Forces applied to the oar during each stroke range from 450-600N in elite male pair rowers (Schneider, Angst & Brandt, 1978). Hosea and Boland (1989) measured compressive loads on the fourth lumbar vertebrae of subjects who rowed Concept 11 rowing ergometers . These loads averaged 4.5 times body weight throughout the rowing stroke. During a rower’s career, these forces produce a protracted strain on anatomical structures. The amount of force exerted and the repetition involved may cause a number of overuse injuries. Low back and knee injuries have been reported to account for 50% of injuries in rowers (Boland & Hosea, 1991). Howell’s (1984) musculoskeletal profiles of 17 elite lightweight women rowers documented five knee, two hip, two wrist-hand, two back, one hamstring, and one ankle injury among the subjects. Biomechanical analysis of the rowing stroke to study injury mechanisms are few in number due to the difficult nature of recording the movement on the water. Land based studies of subjects 2 on rowing ergometers can provide some insight into injury mechanisms but rowing ergometers use a flywheel that is accelerated by the rower starting at the catch position. This is not the same as the actual rowing movement. A rower cannot accelerate the shell at the catch because the athlete must first accelerate the car to equal the speed of the shell system (Celentano, Cortili, Prampero & Cerretelli, 1971; Munroe, 1979; Pannell, 1979). The shell also pitches and rolls during the rowing cycle unlike the stable rowing ergometer. Therefore, study of the actual rowing motion of an athlete in a shell is important in establishing injury mechanisms in rowers. Few kinematic analyses of the rowing stroke have been attempted due to the difficult nature of recording this activity. Kinematic studies of rowing have been limited to two dimensional analysis on rowing equipment, filming from shore, or filming from a motorized launch (Nelson & Widule, 1983; Lamb, 1989; Marindale & Robertson, 1984; Martin & Bemfield, 1980). A two dimensional approach is very limited, especially in sweep rowing, where rotation and three dimensional movements are important components of performance. The development of a videotape technique to study the three dimensional kinematics of rowing, without adding to errors in the Direct Linear Transformation Method employed by the Ariel Performance Analysis System (APAS) will greatly enhance the study of rowing (Ariel, 1993). Once an accurate technique is established, three dimensional analysis can be synchronized with on-board kinetic recording devices to provide a comprehensive understanding of the mechanics of performance and mechanisms of injury. Pumose The purpose of this study was to develop and test the accuracy of a Mobile Video Platform (MVP) that could be towed by a rowing shell. This was done by establishing the movements of the cameras on the MVP with respect to a calibration frame while the MVP was towed by a rowing shell. These camera movements were then mimicked in the laboratory to determine their effect on digitized coordinate data. Hypothesis Movement of the MVP, relative to the shell, will negatively affect the accuracy of the Direct Linear Transformation Method used by the Ariel Performance Analysis System. Definition of Terms Ariel Porformance Analysis SystemiAPAS): computer program used for kinematic analysis in this Study. Blaaa of the 0g: portion of the oar that is in the water and acts as the resistance of a first class lever system at the catch and then as the fulcrum in a second class lever system during the remainder of the drive (Rowing as a lever system is described in Chapter 2). Collar of the oar: portion of the oar that keeps it from sliding laterally in the oarlock. 4 Feathering: occurs as the oar exits the water. The wrist and fingers flex to turn the oar so that the blade of the oar is parallel to the water. Handle of the oar: portion of the oar where force is exerted by the hand. Inboard: the distance from the medial edge of the handle of the oar to the lateral edge of the collar of the oar. Outboard: the distance from the lateral edge of the collar to the lateral end of the blade. Pin and oarlock: swivels on the rigger to allow the oar to travel through an arc. It is the fulcrum of the first class lever system used to bring the oar up to the speed of the shell at the catch. It later acts as the resistance of the lever arm which allows shell propagation in a class two lever system in rowing (Rowing as a lever system is described in Chapter 2.) PM; to skim across the surface of the water. Rigge_r: support on the boat that holds the pin and the oarlock. Sculling: type of rowing in which the rower holds one oar in each hand. Sign; a boat used in rowing. _Slv_e_ep; type of rowing in which each rower holds one oar with two hands. K1398. axis running in the anterior-posterior direction relative to the rower. Lay; axis running in the vertical direction relative to the rower. Z-axis: axis running in the medial-lateral direction relative to the rower. 5 The following definitions have been modified from Martin and Bernfield (1980) to explain the stages of the rowing stroke. Catch: the instant at which the hands begin to move vertically to place the car in the water (see Figure 1.1a). Drive phase: begins with the catch and ends with the finish. This phase is used for propulsion of the shell and consists of the leg drive and the upper body drive. Leg drive: begins with the catch and ends when the rower’s knees are fully extended. Upper body Q've: continuation of the drive phase in which the boat is propelled by trunk extension in combination with adduction of the shoulder girdle and flexion of the elbow. This phase ends when all oars begin to rotate (feather) after being lifted out of the water. Pm period when the wrist begins flexion in order to feather the oar (see Figure 1.1b). Hand and ppper body away; begins with extension of the elbow, abduction of the shoulder girdle and flexion of the trunk. This phase ends when flexion of the knee begins (see Figure 1.10). Seat movement: begins when the rower starts the movement of the seat by flexing the knees and ends when the shank is parallel to the y-axis. Ass—mama o The resistance of the Mobile Video Platform system minimally effects kinematic characteristics of the rowing cycle. Fim 1,1a. Catch. Figpre 1.1c. Hands and upper body away. CHAPTER 2 Literature Review Literature, pertinent to this study, is presented in three categories: two dimensional cinematography, three dimensional methods of analysis, and rowing mechanics. Two dimensional cinematography involves the use of a single motion picture camera to record and subsequently analyze the kinematics of rowing. Three dimensional methods of analysis involves the use and validation of a specific technique for obtaining three-dimensional coordinates of body and object landmarks from two or more cameras simultaneously recording. Rowing mechanics involves a description of rowing technique and mechanics of propulsion of the shell. Two Dimensional Cinematogi'aphy Four studies have used two dimensional cinematography to study the kinematics of rowing (Lamb, 1989; Martin & Bemfield, 1980; Martindale & Robertson, 1984; Nelson & Widule, 1983). Three of the four studies focused on body mechanics, while the fourth focused on the kinematics of the rowing shell. Martindale and Robertson (1984) studied two dimensional segmental energies in rowing a shell and compared them to segmental energies in rowing on an ergometer. Two male and two female scullers were used in their Study. Markers were placed on each subject’s ankle, knee, hip, shoulder, elbow, wrist, and neck. One 16 mm camera filmed the events at 25 frames per second. Martindale and Robertson (1984) concluded that significant differences exist between sculling and ergometry due to differences in 9 energy exchanges between the rower and the equipment. Technical limitations involving the size of the subjects in the field of view were noted by the researchers. Their recommended changes included using a moving camera system when recording rowing to provide a greater number of images as well as a larger subject image in the field of view. The field of view in this study was 20 m and was large enough to film only one complete rowing stroke. Martin and Bemfield (1980) measured shell velocity of the 1976 US. Olympic Men’s Eight by placing markers on the shell and filming with one 16 mm camera at 70 frames per second. The authors found that the velocity of the shell decreased after the catch and reached a minimum at approximately 27% into the leg drive phase. Martin and Bernfield concluded that this decrease in velocity occurred due to the time it takes for the blade’s velocity to equal the velocity of the water moving past the boat. A two-dimensional kinematic analysis of rowing and ergrometry was performed by Lamb (1989) using 30 members of the 1982 Heavyweight Men’s Rowing Team Selection Camp. One 16 mm camera was used at a frame rate of 50 frames per second. The camera was mounted on a motorized launch which followed the crew at a comparable speed. Film images of the toe, ankle, knee, hip, shoulder, elbow, wrist, fingers (oar handle), and head were digitized. The digitized points were used to determine and compare the body segments’ effects on linear oar velocity for rowing and rowing ergometery. Lamb concluded that the trunk is the segment with the greatest effect on linear oar velocity. The filming method used by Lamb (1989) is not possible with three dimensional analysis because cameras need to be fixed relative to one another 10 and to the field of view. This is not possible if cameras are mounted on a motorized launch because the hull speed of a shell cannot be synchronized with a motorized launch. Nelson and Widule (1983) conducted a kinematic analysis on 18 intercollegiate female rowers. The subjects’ rowing experience ranged from four to 40 months. Subjects were filmed at 50 frames per second from one 16 mm camera on a Stanford rowing ergometer. Film images of the toe, ankle, knee, hip, shoulder, elbow, wrist, fingers (oar handle), head and seat were digitized. Nelson and Widule concluded that when the car is perpendicular to the shell, experienced rowers have greater knee angular velocity and a greater sum of trunk and knee angular velocity. These researchers also found that the time between maximum angular velocity of the trunk and maximum angular velocity of the knee was significantly less in skilled rowers. It was concluded that the legs are the primary force producing segment and the trunk has little effect on horizontal oar velocity. This contradicts conclusions made by Lamb (1989). Therefore, further studies of rowing are necessary to determine the effect of body segments on horizontal oar velocity. Three Dimensional Mothods of Analysis Three-Dimensional analysis requires the use of two or more cameras to simultaneously film or videotape an object. The Direct Linear Transformation Method (DLT) is used to take two-dimensional information from two or more cameras and calculate three-dimensional coordinates. The DLT equations are: Xi + lei + L2Yi+ L3Zi + L4 + L9xiYi + Lllxizi=0 311d Yi + LSX, + LsYi + L7Zi+ L8 + L9YIXI+ LIoYIYi 1’ LIIYIZI = 0 l 1 where x i, y i are the film coordinates of the ith point; X ,, Y,, Z, are the object spacial coordinates of the ith point; and L,...L,. contain information on camera orientations and lens and film distortions (Shapiro, 1978). L, L1 1 need not be known but are solved for by using a calibration frame with at least six known Obj ect spatial coordinates (Challis, 1995). The linear least squares technique is applied to solve the DLT equations using the known object spacial coordinates. Shapiro (1978) tested the accuracy of the DLT method for cinematography by using three tests. A control frame with 48 stationary points was filmed. Twenty points were used for calibration in all trials. The first test treated the remaining 28 markers as unknowns. DLT calculations of the positions Of the unknown points yielded an accuracy of 0.51 cm. The second method used the DLT to calculate the length of a meter stick at various locations in the field of view. This method yielded a calculated length within 2 to 4% of the known length. Finally, a free flight golf ball was filmed and the DLT method was used to calculate the acceleration of the ball. The DLT yielded an error of 1 to 4%. Challis and Kerwin (1992) tested the DLT method to determine the accuracy of different shaped calibration frames. After filming the calibration frame, it was rotated 180 degrees and the points were calculated using the DLT method. Challis and Kerwin (1992) concluded the calibration frame need only have points on the edge of the field of view rather than throughout the field of view. Rowing Mechanics In rowing, muscular force is applied to a lever resulting in movement of the rowing shell. Rowing has been described as a first and second class lever system (Celentano, Cortili, Prampero & Cerretelli, 1971; Munroe, 1979; Pannell, 1979). At the catch, the boat is a first class lever system with the pin and oarlock acting as the fulcrum and the water acting as the resistance (see Figure 2.1). As the blade speed matches the shell speed, the lever switches to a second class lever system in which the fulcrum is the center of pressure of the blade and the shell is the resistance (see Figure 2.1). Pannell (1979) stated that if the catch is executed perfectly, the blade will achieve shell speed in the first ten degrees or 0.05 s of the drive. Martin & Bemfield (1980) found that in the 1976 Olympic Men’s Eight it took approximately 0.12 s for the blade speed to match the shell speed. l' f 1st Class lapplied force| laPP led orcel ‘— Lever IE1 water is 2nd Class a being moved Lever shell is being moved Figpre 2.1. The rowing motion as a first and second class lever. CHAPTER 3 Methods The Mobile Video Platform A Mobile Video Platform (MVP) was designed to be towed by a shell (see Figure 3.4). The pontoons for the MVP were designed so that their planing on the water could occur throughout the rowing cycle. The pontoons were made of Styrofoam and covered for protection with epoxy. The platform was designed to allow the boat to pitch and roll through the use of a Specialized hitch that was attached to the gunnels of the boat (see Figure 3.1a & b). Wooden supports were attached to the pontoons which then connected to two pieces of 1.27 cm aluminum box tubing (see G & H in Figure 3.2 a & b). This tubing provided a stiff connection between the pontoons. 1.63 cm right angle aluminum shafts connected the platform to the hitch (see F in Figure 3.2 a & b). The length of separation of the pontoons (227.5 cm) was set at a distance that did not interfere with the oar or shell. Movement in the MVP relative to the cartesian coordinate system fixed to the shell occurred along the x, y, and z axes and in the xz, yz, and xy plane. Movement along the x-axis occurred from lack of stiffness in the materials when the system accelerated. This was minimized by using materials and connections that yielded little under the stresses encountered. Movement along the z-axis occurred from looseness in the connections of the hitch to the pontoons and from the hitch to the shell. This was minimized by tightening connections before testing. 1 3 Figaie 3.1. Specialized hitch to allow the shell to pitch and roll. Figpre 3.2a. Three dimensional View of the MVP. A: hitch E: right pontoon H: 1.27 aluminum box tubing B: lefl camera F: 1.27 cm right angle aluminum 1: line attached to the shell C: right camera G: wooden supports J: wooden slats D: left pontoon 219.0cm 118.0 cm 61.2cm 28.5 cm Figpre 3.2b. Top view sketch of the MVP. 16 Movement in the xz plane occurred through rotation of the MVP about a vertical axis through the hitch. This was minimized by connecting the hitch to the shell at two locations, keeping the pontoons parallel to one another, using stiff building materials and by using a line which was attached from the rear piece of the 1.27 cm box tubing on the MVP to the shell (see Figure 3.2a). Movement in the xy plane and along the y-axis occurred as a result of accelerations of the shell and water resistance on the pontoon. As the MVP was, positively accelerated, the bows of the pontoons lifted up and out of the water causing a rotation about a z-axis through the calibration frame in the xy plane. Likewise, the bows moved downward towards the water when the shell was decelerating. This was minimized by designing the platform to plane on the water through the entire stroke cycle. Movements in the xy plane were further minimized by designing the connection from the hitch to the MVP to be as linear as possible (see F in Figure 3.2a). This kept forces applied from the shell to the MVP from adding to angular accelerations of the MVP. Movement in the yz plane occurred as a result of wave activity. Waves effect the pontoons unequally and cause the MVP to rotate. This was minimized by testing during calm water conditions. Movements in the xz plane, yz plane and along the x, y and z axes were minimized but caused systematic error in the data. These errors were examined in order to determine their effect on the accuracy of three dimensional cartesian coordinates derived from two dimensional images by two cameras mounted on the MVP. 17 Pilot Study A pilot study was conducted to determine the effects of MVP movement on the quality of the video images taken from the MVP. A single scull was the shell of choice for this study because success of planing at the lower hull speeds of a single would allow the MVP to be used on any shell. The pilot study was performed on a male single sculler who had ten years of competitive rowing experience. The sculler was 172.7 cm in height and weighed 69.5 kg. Cameras were placed on the MVP and video was taken of the sculler. The videotape of the sculler was digitized but problems arose in this process. Movements in the MVP, especially during the leg drive, made the results suspect to error. This was due to the MVP falling from its plane on the water. This coincides with Martin’s (1980) finding that the lowest shell velocity is achieved during the leg drive. An eight oared shell rather than a single scull was used in the actual testing so that the MVP would remain planing through the entire rowing cycle. Also, the resistance of the MVP was distributed among the eight rowers. This minimized the effects of resistance of the MVP on the rowers. Other problems that arose during the pilot study included: 1. a lack of an adequate synchronizing event for the cameras causing difficulty when digitizing the two camera views, 2. errors in measuring points on the calibration frame causing errors in the digitized information, and 3. a lack of markers on the shell and on anatomical landmarks of the rower causing inaccuracies in the digitization of the video images. 18 Changes were made from the methods used in the pilot study to limit these problems. These changes included: 1. adding markers to locations that were digitized to allow easier tracking of these video images,] 2. increasing precision in measurements Of calibration points through repeated measures , 3. adding a synchronization event involving the coxswain popping a balloon over her head when in the field of view and 4. making the connection from the shell to the pontoons more linear so that movements in the shell had less effect on movement in the MVP. Videotaping MVP Movement When In Tow Calibration Frame A calibration frame was constructed from 3.81 cm diameter PVC pipe and floated on the water. The calibration frame was square (6.14 m by 6.14 m). A 1 m piece of 1.27 cm diameter PVC pipe was vertically attached at each corner Of the square. Markers were created on these vertical pieces by spray painting the pipe black then adding five 1.5 cm white stripes to the pipe. Stakes were placed on the inside comers of the calibration frame and driven into the river bed to hold the frame in place when videotaping and to act as guides for the coxswain to steer the shell between when the calibration frame was removed (see Figure 3.3). The size of the calibration frame was chosen because it allowed the markers on the calibration frame and the MVP to be easily tracked during digitization. However, it took less than one rowing stroke to cover this distance. In order to reconstruct the movements of the MVP through an entire rowing cycle, multiple trials were conducted. Figpre 3.3. Calibration frames with stakes. M Five markers on the MVP were digitized: two markers on each camera (right camera front and back and lefi camera front and back) and one marker on the shell (see Figure 3.4). The markers were white Styrofoam balls with a diameter of 2.54 cm. The MVP was painted black to enhance the contrast with the white markers. The marker on the shell was mounted to a piece of black painted plywood. A: Shell marker B: Right camera front marker C: Right camera back marker D: Left camaa front marka E. Lcfi camera back marker ‘ Figpre 3.4. Five markers used to study the movement of the MVP. 20 Videotaping and Digitizing First, the calibration frame was videotaped then removed. Then the rowers were instructed to row the shell at 34 strokes per minute starting 100 m before the stakes and ending ten strokes beyond the stakes. The stroke rate was held constant through the use of a Nielson Kellerman Cox Box. This rate was chosen because it is a typical stroke rate used in collegiate racing. Two Panasonic AG455P video cameras, which operated at sixty fields per second with a shutter speed of 1/2000 5, were mounted on tripods and located on shore to record the calibration frame, shell, and MVP. The cameras were separated by a distance of 41.1 m. The right camera was 32.7 m from the right front stake of the calibration frame and the left camera was 38.1 m from this same stake. Next the shell and MVP were videotaped as they passed through the space previously occupied by the calibration frame (see Figure 3.5). The coxswain of the shell popped a balloon over her head while in the cameras’ fields of view. The first field in which the balloon popped was used for synchronization of the two video records. The field of view was too small for a complete rowing cycle to be videotaped within it. Therefore, multiple trials were used to capture the movements of the MVP throughout two rowing cycles. Seven trials were recorded but only trials 1 and 5 captured a complete drive phase and only trials 2 and 6 captured a complete recovery phase. These four trials were used to reconstruct movements of the MVP over two rowing cycles. Events of the rowing cycle: the catch, leg drive, upper body drive, finish, hands and body away and seat movement, were observed from the videotape and recorded for each trial. These events provided reference points when tracking the movements of the MVP during the rowing cycle. 32.7 m ,L__,_. shoreline Figaro 3.5. Top view sketch of the videotaping area. 22 The video of the right and left, front and back camera markers and the shell marker were digitized for each of the four trials using APAS. The catch was used as the beginning event of the drive phase and the ending event of the recovery phase. The finish was used as the beginning event of the recovery phase and the ending event of the drive phase. Nine frames were taken before and after the beginning and ending event for each trial. Trials 1 and 5, the drive phase, consisted of 64 and 70 frames, respectively. Trials 2 and 6, the recovery phase, consisted of 75 and 76 frames, respectively. The raw data was then used to calculate movements of the MVP. Caloilation of MVP Movements The digitizing error was estimated by calculating the distance between the right camera’s front and back markers and the distance between the lefi camera’s front and back markers for each frame. Maximum and minimum values of the distance between markers were taken from these calculations. The greatest difference of the minimum and maximum x, y and 2 value was used as the maximum value of digitization error. Movements along the x-axis were calculated by subtracting the x-coordinate of the front camera markers for each camera and the x-coordinate of the shell marker for each frame. The maximum and minimum values of the distance between the front camera markers and the shell marker were taken for each trial. The greatest difference of the maximum and minimum values of the distance between the cameras and the shell was used as the movement of the MVP with respect to the shell along the x-axis. 23 Y-axis movements were defined as the greatest difference in maximum and minimum y-coordinates for each camera’s front markers for each trial. Z-axis movements were difficult to account for because the shell was allowed to roll in the yz plane. Movement of the MVP along the z-axis relative to the shell was established in the following way: 1. The change in the z-coordinate from one frame to the next was calculated for the shell marker. 2. The change in length along the z-axis between the right camera’s front marker and the shell was calculated from one frame to the next. 3. The change in length along the z-axis between the left camera’s front marker and the shell was calculated from one frame to the next. 4. The sum of 2. and 3. was calculated. The greatest difference in maximum and minimum values from 4. was used as the movement of the MVP with respect to the shell along the z-axis. .V‘ Movement of the MVP in the xz plane was estimated by calculating the arctangent of the (x-axis movement) / [(length of the MVP from the midpoint to the camera) - (z axis movement)] (see Figure 3.6a & b). The greatest difference in maximum and minimum values of the arctangent was used as the movement of the MVP in the xz plane. Movement of the MVP in the yz plane was estimated by: 1. Calculating the difference in the y coordinates and the z coordinates of the right camera’s front marker and the left camera’s front marker, and the right camera’s back marker and the left camera’s back marker for each frame. 2. From 1., calculating the arctangent of the (difference in the y coordinate)/ (the difference in the z coordinate) for each frame. 3. The greatest difference between the maximum and minimum of 2. was used as the estimate of movement of the MVP in the yz plane. Movement of the MVP in the xy plane was estimated by: 1. Calculating the difference in the y and x coordinates of the right camera’s front marker and the right camera’s back marker, and the left camera’s front marker and the left camera’s back marker for each frame. 24 2. From 1, calculating the arctangent of the (difference in the y coordinate)/ (the difference in the x coordinate) for each frame. ‘ 3. The greatest difference between the maximum and minimum of 2. was used as the estimate of movement of the MVP in the xy plane. left camera midpoint between A x cameras ('1. /_ right camera "ST .52 .dx ‘- 0. fldz . z mdpt of distance ll between cameras to dz: calculated maximum 2 axis movement dx: calculated maximum x axis movement Figiao 3.6. a. Positive and negative MVP movements in the xz plane. b. Diagram of variables used to solve for movements in the xz plane. Treatment of the Movements of the MVP Maximum and minimum displacements of the MVP along the x, y and z axes and in the xz, yz and xy planes were taken from the digitized data. These data were used to establish the range for laboratory tests on the uncertainty in digitized data when movement occurs in the cameras. Movements of the MVP were linked with events of the rowing cycle to establish how the MVP responds during different portions of the cycle. This was important because the pilot study showed jostleing of the cameras during the initiation of the leg 25 drive phase but little problems elsewhere in the stroke. During the first half of the leg drive phase, the Shell’s velocity was minimum which caused the pontoons to stop planing. An eight oared shell was used to maximize the minimum speed thereby minimizing movement in the MVP during this phase. Establishing Control Coordinates Calibration Frame A PVC calibration frame, 1.68 m by 0.79m by 0.83 In , included 12 points on the edges of the field of view of each camera. Eight extra markers were attached to the calibration frame (see figure 3.7). The coordinates of these extra markers were measured then treated as unknowns in the digitization. The calibration frame was placed so that it was a comparable distance (2.90 m from the cameras to the front edge of the frame) from the cameras as a rower was from the MVP cameras in the shell. The calibration frame was videotaped by the two cameras. The cameras used for videotaping were Panasonic AG455P The cameras ran at 60 fields per second with a shutter speed of 1/200 5. A 46 degree angle existed between the cameras and the midpoint of the front lower edge of the calibration frame(see figure 3.7). 26 o - calibration points 0 - points, A-H, treated as W... Y x 0.79‘ 2 To the In To the left 46 right F igare 3.7. Calibration frame and points treated as unknowns. The points treated as unknowns were digitized and the locations of these points were calculated using APAS. The locations of these positions were treated as the control coordinates to establish the amount of uncertainty in digitized coordinates when movements occur in the cameras. Esiablishing Uncertainiy of the MVP Systematic testing of the changes in known spatial coordinates due to changes in camera positions were examined in the laboratory. Tests on movement of cameras along the x, y and z axes and the xz, yz and xy planes were examined by using incremental changes along these parameters and by comparing digitized values with the control coordinate values. The uncertainty in the system was calculated as follows: U,“ = 2x/2X dX’+2x,/.‘2Y dY’ + flit/22’ dZ + fag/20 d0’ + Ex/Bd) drb’ + 2x, lfl‘I’ d‘I” U,, = .‘Zy,/2X dX’ + 2y,/2Y dY’ + 2y,/rz dZ’ + 2y,/20 d0’ + 2y,/2d> dd)’ + 2y, lfl‘I’ d‘I” U2, = fizflX dX’ + flz/EY dY’ + flzilfll dZ’ + 325/20 d9’+ 22/24) d¢’ + 22, IE‘I’ d‘I” where 27 U, is the uncertainty in the digitized x coordinate, Uy is the uncertainty in the digitized y coordinate, U2 is the uncertainty in the digitized z coordinate, i is the digitized point A, B, C, D, E, F, G or H x is the digitized x coordinate, y is the digitized y coordinate, z is the digitized z coordinate, X is the change in position of the cameras along the x-axis, Y is the change in position of the cameras along the y-axis, Z is the change in position of the cameras along the z-axis, 0 is the change in position of the cameras along the xz plane, if is the change in position of the cameras along the yz plane, ‘1’ is the change in position of the cameras along the xy plane dX’ is the maximum change in the cameras along the x-axis when towed by the shell, dY’ is the maximum change in the cameras along the y-axis when towed by the shell, dZ’ is the maximum change in the cameras along the z-axis when towed by the shell, d0’ is the maximum change in the cameras along the xz plane when towed by the shell, d¢’ is the maximum change in the cameras along the yz plane when towed by the shell, and d‘I” is the maximum change in cameras along the xy plane when towed by the shell. The partial derivatives listed in the uncertainty equations were solved empirically and therefore, could only be estimated because measurable increments were used rather than infmitesimally small increments. The partial derivatives were estimated by: 2 Hi / 2 Q = (In, / d Q where n is x, y, or z, i is the digitized point A, B, C, D, E, F, G, or H and Qis X,Y, Z, 0,4) , or‘I’. dni = ni " ni control where n, com. is the control x, y or z coordinate of the ith point and dQ is the camera movement in X,Y, Z, 9, d) , or ‘I’ By estimating the partial derivatives 2 n, / .‘2 Q with dn, / d O, the affect of each camera movements on the total uncertainty was estimated. These pinpoint areas of concern in movements of the MVP. 28 Measuring X,Y, Z, 9, o, and ‘I’ A Floor Mounting Board (FMB) was constructed to allow a change in one of X,Y, Z, 9, (b or ‘I’ while holding the other parameters constant (see Figure 3.10a). The FMB was made of two 60.96 cm by 10.16 cm by 10.16 cm boards. Hinges were mounted to these boards to allow rotation in the xy and yz planes (see Figure 3.10b). Holes with a diameter of 2.54 cm were drilled into the FMB in two directions: along the x-axis and in an are centered at the midpoint of the FMB (see Figure 3.10c). Two cameras were then mounted to a 5.08 cm by 10.16 cm by 304.80 cm board known as the Camera Mounting Board (CMB). Four holes with a diameter 2.54 cm were drilled into the CMB (see Figure 3.10c). A 2.54 cm dowel was place through two of the holes and into the FMB (see Figure 3.10a). An adjustable aluminum bracket kept the CMB from sliding on the dowel and allowed the CMB to be moved along the y-axis (see Figure 3.10a). The CMB was moved through the dQ values listed in Table 3.1 for each Q: Table 3.1. dQ values for each Q. Q dQ values X (cm) -18.0, -l4.4, -10.8, -7.2, -3.6, 0.0, 3.6, 7.2, 10.8, 14.4, 18.0 Y (cm) -10.0, -8.0, -6.0, -4.0, -2.0, 0.0, 2.0, 4.0, 6.0, 8.0, 10.0 Z (cm) -18.0, -14.4, -10.8, -7.2, -3.6, 0.0, 3.6, 7.2, 10.8, 14.4, 18.0 9 (deg) -10.0, -8.0, -6.0, -4.0, -2.0, 0.0, 2.0, 4.0, 6.0, 8.0, 10.0 4) (deg) -9.3, -5.9, -3.9, -l.9, 0, 1.9, 3.9, 5.9, 9.3 ‘1’ (deg) -10.3, -5.9, -3.2, -3.0, O, 3.0, 3,2, 5.9, 10.3 29 Definitions of positive and negative angles Of 0, (p, and ‘I’ are shown in Figures 3.6a, 3.8 and 3.9, respectively. Measurements were taken at each increment, dQ, for each plane or axis movement, Q. Ten fields of video were then digitized using APAS. The digitized information was used to establish the effect of camera position and orientation on the digitization of known spatial coordinates. Right camera 0 O 0 u I i D O D o O c O O I u. U 1 Right camera ‘o ....... """"""" l Figaro 3.9. Positive and negative MVP movements in the xy plane. I ' ' I t .M. W Floor Moun ng Board Figare 3.10a. The Floor Mounting Boards and the Camera Mounting Board as seen from the calibration frame. Hinge to allow xy rotation Figpre 3.10b. Right half view of Camera Mounting Board and Floor Mounting Board as the system is rotated in the yz plane. 2.54 cm hole for 2.54 cm dowel when - ' g measurements in the xz plane 4 cm hole for 2.54 cm dowel ,when taking measurements along 5 . C X-lXIS Figare 3.10c. Top view of right Camera Mounting Board and right Floor Mounting Board. Treatment of the Laboratog Data The ten fields of video for each Q at each dQ value were digitized. The partial derivatives .‘2 n, / .‘2 Q were estimated from the calculations of dn, / d Q. The uncertainty equations were analyzed to determine the weight of each Q on the uncertainty of the movements of the MVP. Finally, the uncertainty of the MVP was calculated. CHAPTER 4 Results Five points on the MVP were digitized using APAS. The coordinates for these markers are listed in Appendix A. Trials 1 and 5 represent recorded events during the drive phase of the rowing cycle. Trials 2 and 6 represent recorded events during the recovery phase of the rowing cycle. Effects of the Rowing Cycle Events on MVP Movements The movements of the MVP were plotted for each frame to determine the effect of rowing events (catch, leg drive, upper body drive, hands and body away and seat movement) on the movements of the MVP. Figure 4.1 a,b and c shows the movement of the MVP along the x, y, and z axes. Figure 4.2 a,b and c shows the movement of the MVP along the xy, yz and xz planes. No distinguishable patterns linking rowing events to erratic MVP movements were found. Instead, erratic movements were found throughout the rowing cycle. This may be due to the large field of view used to track the MVP. A smaller field of view would increase the accuracy of the digitization. This would provide greater insight into the effects of the shell movement on the movement of the MVP. 32 33 X-AxisMovementofthe RightCamera'sFrontMarker During The Drive Phase 174.0 end of leg drive 172.0 "m" finish 170.0 '5" 168.0 =3 +Trial1 g +Trial5 > 166.0 0 2 164.0 1 162.0 D on t leg drive 13°~°..¢...:.¢ .............. :..:: .......... :...¢:::.... " '9 °’ 3'2 t: a R '8 ‘3 "4’ 9 From o(0.0167 slfram e) X-Axis Movement ofthe Right Camera'c Front Marker During The Recovery Phase 180.0 " beginning of seat movement 1750;: +7...” - Trials , 'IDIDI’I catch 4» E 170.0 4.. :2: .. > .. 0 165.04 3 160.0. \ beginning of seat movement 155-0 HH::¢H:H4¢HH;;:H;::::tH::t:::::;;:::::::::::H: ""’ “fitERR88393 BIB Fram o(0.0187 cltram e) Figaro 4.1a. Movement of the MVP relative to the shell along the x-axis. 34 Y-AxisMovementofthe RightCamera'sFrontMarker During The Drive Phase 50.0 end of leg drive catch finish .. .. i ‘ g 45.0 -. ' I" . 3 ,_ E _."’ Til.” end of leg drive +Triai5 40-0 :tti4iti:tfi:‘.:it¢¢ti¢t:::¢¢tiitfitit‘rtiiit:tfttt - m a :2 z: a e s s s From o(0.0187 stirsm e) Y-Axls MVP Movementotthe Right Camera's Front Marker During the Recovery Phase 48.0 beginning of seat movement 46.0 ‘1‘II l i if i ‘ 44.0 &\~ I ‘5‘ tiish a: catch 2 42.0 4.. i 40.0 -- —_—tr.isl.2—1 beginning of seat movement + 38.0 # wtrisle 35-0 HHHHHH;::::::;::;;;:::;:::::::;:4:4:::t:::::t:tt: " Fams(0.01§7sltrsm:) '0 Figiao 4,1b. Movement of the MVP along the y-axis. 35 Z-Axis Movement ofthe MVP Relative to the Shell During the Drive Phase 10.0ca'tch end offi drive end of leg drive finish 5.0 t‘ ‘ ‘ F . I I l ‘5‘ . 0 j , I 'H, 3 ' r 0.0 , l, l l ‘n i, A." Err-H... O s .. -5.0 + -O-Triel1 . Trials -1o.o Frsm e(0.0167 slfrsm e) Z-Axis Movement of the MVP Relative to the Shell During the Recovery Phase beginning of seat movement Movementicm) {a 'o O-I-I-1:_ 5 I: 13 25 '4.0 up. .—.—tris12 '6'0 '“ ~I~wm|6 8 0 beginning of seat movement 40.0 Frsm “0.0167 slirsm e) Figare 4.10. Movement of the MVP relative to the shell along the z-axis. 36 XZ Plane Movements ofthe MVP During the Drive Phase 4.0 teh end of leg drive 3.0 ._ g + triel1 «ml-- trial 5 “"3” 2.0 .t .. l , . .4 A r .m ,. . n =, u v n - :2 : ii a a -1.0 .. ' l -2.0 .. j . l . end of leg drive 5; MVP Movement(degrees) o o ¢l a -4.0 Frsme(0.0187slireme) XZ Plane Movements ofthe MVP During the Recovery Phase 4.0 than beginning 01 seat movement cs ch 3.0 -_ +trisl2 ‘fl +~trie16 2.0 4- 1.0 -_ O 0 a PA .. .- j A 4 -2.0 . i _ . i -3.0 I beginning of seat movement v.‘ MVP Movementidegrses) 1 11 21 Frsm e(0.0107sltrsm e) Figtae 4.2a. Movement of the MVP relative to the shell in the xz plane. 37 YZ Plane Movements ofthe MVP During the Drive Phase 0.8 cietch ;( 0.6 -. ‘ _ \ finish 3 0'4 .. end of leg dr~ - 8 3 E 02 -. 3 2 0,0 ,I. . he . l ,v-valwceaaasss -0.2 +trisl1 -~.--triel5 -0.4 Frsme(0.0187sltrsme) YZ Plane Movements otthe MVP During the Recovery Phase 0.2 {nigh beginning oiseet movement cs ch 0'1 -- —0—-trisl2 ~O-trial 6 0.0 - ,, fl a v. i! .. 3W3. -0.1 . P ' fl’ “iii i; : 9 ., j; i ' 1 E -0.2 I .5 li é -o.3 )- s -0.4 , I fl : '0.5 E - -0.6 beginning of seat movement -0.7 -0.8 Frsm e(0.0187sltrsm e) Figare 4.2b. Movement of the MVP in the yz plane. 38 XY Plane Movements ofthe MVP During the Drive Phase 3.0 tch end of leg drive __._i.rial1 2-5 -~ __-__trial5 2.0 __ . 1; i finisli E 1.5 -. , ’ h 8' . , 3 . u 1.0 " V ' i "r t 'l’ o . a 0.5 s ‘ t 0.0 - In - n N In ('0 V v I ‘ A F ' s- v- K N a 1') ' B Q ») -o.5 ._ I end of leg drive -1.0 From e(0.0167sltrsm 0) XY Plane Movements ofthe MVP During the Recovery Phase 3.5 tnish beginning 01 seat movement catch 3.0 -» . + trial2 «Ow-trials 2.5 .. g 2.0 ' r l 3 . E 1.5 ‘ 5 r 1 .» 3 A l s 1.0 . I . ) s ' l - I 0.5 , 0 0 ‘ beginnin 01‘ seat movement . ', . '0 l 2 a a a 8 s 8 :5 s -0.5 _ Frsm e(0.0167sltrem e) Figiao 4.2c. Movement of the MVP in the xy plane. 39 Maximum Movements of the MVP Table 4.1 lists the maximum movements of the MVP and the average digitizing error for the four trials used in the MVP analysis. Table 4.1. Movements of the MVP from the digitized data. Digitizing(cm) X(cm) Y(cm) Z(cm) 0(deg) 4) (deg) ‘I’(deg) x:5.6, y:0.9, z: 7.8 17.4 10.0 16.6 8.9 2.9 6.6 The large digitizing error along the x and z axis can be attributed to the large field of view. This large error corresponded with large MVP movements along the x and z axes and in the three planes. The y-axis was approximately 1/20 the length of the x and z axes. This resulted in a smaller digitization error for the y coordinates. The calculations for the movements of the MVP are in Appendixes B through H. A table of movements of the MVP for all trials is listed in Appendix I. The values from Table 4.1 set the maximum values for testing in the laboratory. However, the calculation of the MVP movements did not distinguish between positive and negative values but gave only a range of values. Therefore, the values used in the laboratory were moved through the positive and negative range of values. The range of values used for the camera movements(Q) with respect to the control frame are listed in Table 4.2. 40 Table 4.2. Range of values used in laboratory testing. X(cm) Y(cm) Z(cm) 0(deg) ¢ ‘I’(deg) ’ (deg) |+/-18 +/-10 +/-18 +/-10 +/-9.3 +/-10.3| Uncertaing Measurements Ten fields of video were taken of the eight unknown points: A, B, C, D, E, F, G and H for each Q at each dQ value (see Appendices J-Q). The average x, y and z coordinates were taken from the digitized fields for each Q at each dQ value (see Appendices J-Q).] These average coordinates were used as n, in the equation dn, = n, - 1116611661- The values dn, / dQ were then calculated. Analysis of the dn, / dQ values showed constant traits. Therefore, the average of the tin, / dQ values were taken for each point at each Q (see Table 4.3). Analysis of the average dn, / dQ for each point showed similarities across points A, B, C and D and E, F, G and H. Therefore, the average dn, / dQ values for points A through D and B through H were calculated and were used to approximate the partial derivative in, / 2Q (see Table 4.3). Two sets of uncertainty equations, one for points A, B, C and D and one for points E, F, G and H, were written. These equations are: Um, = 1.12 dX’- 0.28 dY’ + 0.63 dZ’ - 1.21 d0’ — 0.12 d0’ + 2.15 as” U,“ = 0.04 dX’ + 0.01 dY’ + 0.22 dZ’ - 0.46 d0’ + 0.01 (10’ + 0.39 as" U,A.D= .017 dX’ + 0.48 dY’ - 0.04 dZ’ + 0.01 00’ + 0.55 d¢' + 0.02 d‘I” U,,m= -0.12 dX’ + 0.03 dY’ - 0.02 dZ’ + 0.04 d0’ + 0.31 d¢’- 0.15 0‘!” UM= -0.12 dX’ + 0.02 dY’ + 0.42 dZ’ + 0.36 60’ -0.78 11¢: - 0.13 d‘I” UM= -0.09 dX’ + 0.02 dY’ + 0.03 dZ’ - 0.09 d0’ -0.49 11¢: - 0.13 as” 41 Table 4.3. Average dn,/dQ. -_ l _ I A a c 0 Average: pointsA-D n x y z x y z x y z x y z x y z F # dm/dx 1.00 0.00 0.28 1.17 «0.33 -0.22 1.25 —0.02 -0.01 1.05 -0.33 0.03 1.12 -0.17 -0.12 m dni / dY -0.10 0.42 0.01 -0.10 0.51 0.00 -0.84 0.56 0.09 -0.07 0.44 -0.02 «0.28 0.48 0.02 dry] (12 0.81 0.02 0.30 0.59 -0.1 1 0.45 0.81 0.05 0.41 0.21 -0.04 0.43 0.63 -0.04 0.42 any .19 42.01 -0.10 0.45 -177 026 0.36 .072 .005 0.37 .035 ~0.06 0.26 -121 0.01 0.30 ‘W‘ .019 0.95 -0.46 0.06 0.61 4.19 0.02 0.34 .037 0.56 0.00 -105 0.12 0.55 -0.76 ‘m‘ 1.34 0.29 -0.46 2.66 .023 -027 221 024 -0.02 2.16 .023 024 2.15 0.02 -0.13 I i F 5 H Average: pointTE-J-l—I n x y z x y z x y z x y z x y z dm/dX 0.06 -0.01 0.00 0.04 .024 .002 0.06 .0.01 -0.14 0.00 .023 .020 0.04 .0.12- .000 dn./dY -0.02 0.04 -0.04 0.03 0.02 -0.03 0.02 -0.01 0.00 0.02 0.07 -0.01 0.01 0.03 -0.02 dry/a 0.03 -0.01 0.04 0.04 -0.01 0.02 0.34 0.01 0.03 0.48 -0.09 0.05 0.22 -0.02 0.03 l dn,/ d9 -0.02 -0.02 0.00 -0.11 -0.04 -0.16 -0.80 -0.06 -0.16 ~1.04 0.28 -0.m -0.46 0.04 -0.09 0.” 0.01 -0.10 030 -0.01 -0.82 -0.22 0.51 -0.18 ‘0.04 0.73 .030 0.01 0.31 -0.49 0.10 0.06 -0.01 0.02 -0.29 -0.03 0.04 0.02 -0.30 1.33 -0.37 -0.18 0.30 -0.15 -0.13 3 s 3 % The contribution of each dnildQ to the sum of the dn,-/dQ values for each coordinate was examined to determine the weight of each camera movement on the uncertainty equation (see Table 4.4). The Q’s with the greatest affect on the uncertainty for points A through D were: 1. ‘I’, 39% of the total dx/dQ, 2. d) and Y, 81% of the total dy/dQ and 3. it, 42% of the total dz/dQ. The Q’s with the greatest affect on uncertainty for points E through H were: 1. ‘I’ and 0, 75% of total dx/dQ, 2. (I), 46% of the total dy/dQ and 3. d), 57% of the total dz/dQ. UK M, was the only equation with dx/dQ values greater than one. This means that small camera movements cause large errors in the digitized data. These large dx/dQ 42 values were not present in UK 1.3,“. This is due to the increase in angle between the cameras and the field of view. Table 4.4. Percent of total dn/dQ. Points A-D Percent Total danQ olnts 241 Percent Total danQ n x y z n x y z dn.l dX 20 11 7 dn1/dx 3 16 10 dnjl av 5 u 1 dnil av 1 5 2 dm/ d2 11 3 23 61).] d2 20 4 4 6n./ d0 22 1 20 dn./ d0 41 6 11 611.1 a. 1 46 42 dnl 11¢ <1 96 46 67 611. / or 19 1 7 dn. / 11‘? a4 22 16 Uncogm of the MVP Using the maximum values from the MVP movement and assuming that these movements have the same sign as the average dn,/dQ. The maximum uncertainty values obtained for the MVP were: UxA-D = 58.1 cm UyAJ): 10.3 cm Uni): 15.6 CI“ ngnr' 11.10111 UyAJ): 5.0 cm U133: 13.5 Cm Points at the finish position of the rowing cycle will have greater uncertainty than points at the catch. However, the uncertainty at either position is too great for any biomechanical model since these errors would be amplified with velocity measurements. Structural changes to the MVP are necessary to limit movement of the MVP along the x-axis and reduce rotations in the xy and yz planes. Errors can be substantially decreased by either moving the MVP closer to the rower or increasing the distance 43 between the cameras. Either option would increase the angle between the cameras and the rower in the field of view. CHAPTER 5 Discussion The analysis of the MVP while under tow by the shell yielded large movements and large digitizing error, especially along the x and z axes. These large errors corresponded to a large field of view in the xz plane. Digitized data of the MVP showed erratic movements throughout the rowing cycle. The laboratory tests on affects of camera movement on digitized data showed that proper triangulation between the cameras and the field of view greatly minimized the uncertainty. For points that had approximately 46 degrees between cameras, movements along the xz and xy planes were the major contributors to the uncertainty in the digitized x coordintates. Movements along the yz plane were the main contibutor spelling to uncertainty in y and z coordinates. Re cin no 0 Mountin Cameras to the Shell The derived uncertainty equations: UxA-D = 1.12 dX’- 0.28 dY’ + 0.63 (12’ -1.21d0’ - 0.12 d4)’ + 2.15 d‘I”, UxE-H = 0.04 dX’ + 0.01 dY’ + 0.22 (12’ - 0.46 dB’ + 0.01 d¢1’ + 0.39 d‘l”, UyA—D = -0.17 dX’ + 0.48 dY’ - 0.04 dZ’ + 0.01 d6’ + 0.55 dil)’ + 0.02 d‘f”, UyE-H = -0.12 dX’ + 0.03 dY’ - 0.02 dZ’ + 0.04 dB’ + 0.31 d¢’- 0.15 d‘I”, UzA-D = -0.12 dX’ + 0.02 dY’ + 0.42 dZ’ + 0.36 dB’ -0.78 d¢’ - 0.13 d‘I”, and UzE-H = —0.09 dX’ + 0.02 dY’ + 0.03 112’ - 0.09 d0’ -O.49 dili’ - 0.13 d‘f” show that the MVP’s three degrees of freedom caused great inaccuracies in the digitized data. The uncertainty of digitized data could be greatly reduced if the cameras were attached directly to the shell, rather than towed by it (see Figure 5.1). Attaching the cameras would limit rotations of the cameras to the yz plane. By establishing proper triangulation between the cameras and the field of view the uncertainty equations could be reduced 44 4S to the following: Ux = 0.01 dd)’, Uy = 0.31 dd)’ and Uz= 0.49 dd)’. aluminum tube mounted to the shell a camera mounted to ' \ aluminum tube r ‘ / camera mounted to alumnium tube Figiae 5,1. Top view sketch of cameras attached directly to a shell. The main disadvantage of attaching the cameras to the shell is the inability to calculate the rolling of the shell from digitized data. However, a goniometer could be used to measure the rolling of a shell that corresponds to each field of video. This would allow the uncertainty of each field to be calculated. 46 Another disadvantage is the possibility of balance problems caused by suspending cameras from the shell. This is especially true for small boats such as singles and doubles because the weight of the shell is much smaller than an eight or four person shell. Lightweight cameras could be used to limit this problem. Advantages of a Qmera System Attached Directly to a Shell The greatest advantage of attaching a camera system to a shell is the increase in accuracy, especially along the x-axis. The rowing motion takes place mainly in the xy plane. The MVP had large movements in this plane causing large errors in the digitized data. The error in digitized x-coordinate data that was caused by camera rotations in the yz plane was minimal. A second advantage is that a shell mounted system would be much lighter than the MVP and would not drag in the water. This means that testing can be done in less than ideal rowing conditions (i.e., smooth water). Estimated Error in Kinematic Calculations when Cameras Rotate in the YZ Plane The calculations that are most uncertain when calculating kinematic variables from digitized information are linear and angular accelerations. Table 5.1 leads through the calculation of the uncertainty in linear and angular accelerations given a rotation in the yz plane of five degrees. Five degrees was chosen as a better estimate of yz rotations. The calculated 10.3 degrees would make the riggers submerge in the water, which did not occur. 47 Table 5.]. Calculation of the uncertainty in linear and angular acceleration given a rotation in the cameras of five degrees in the yz plane. Linear Angular TefiLnitions a: linear accleration an: angular acceleration At: time between frames 6: segment angle x: x coordinate(y or 2 could also be At: time between frames used) x: x coordinate(y or 2 could also be i: frame number used) y: y coordinate(x or 2 could also be used) i: frame number equations an = xi+1~ 2Xi + Km / M 9i: ’tan'1 (Yi - m) / (Xi - Km) from Winter(l990) mei = a... - 29i + 9H / A? from Blatt(l986) and Winter(l990) uncertainty 5 (365) = [5(Xa+i)‘ + 25(Xa)‘ + 5("i- 5 (9i) = [50%)1 + 5(yi-1)‘ + 5(Xa)‘ + 5(Xa- equation 02] 021‘ 6 («99 = [5(9a+1)2 + me? + 6(9...)’1"2 assumptions proper triangulation and small proper triangulation and small movements yield: movements yield: 5(Xi+1) = 6(Me) = 509.1) 5(yi) = 50m) and 5(Xa) = 509.1) and 5(9m) = 5(9a) = 5(9a.1) uncatainty 6 (31d) = 2 5(x9 8 (6i) = [2 My)2 + 2 50:91]"1 equation 6 (0.99 = 2 5(6i) after 199mm“ Given yz 5(x9=0.01 cm/deg (5 deg)= +/- 9 in g 9 in xz 9 in y; rotation ors 0.05cm 5(ei)=+/- 6(eo= +/- 5(eo=+/- de ._ = _ 3.4 de , 4.1de , m 6(y)— 0.31 cm/deg(5deg) +/ 1.55 2.1 deg: 8 ((1603: 5 (one): cm 5 (gel)— +/. 6 8 deg/s2 +/. 8 2deg/s2 6(zi)= 0.49 cm/deg(5deg) = +/- 2.45 +/-4.2 ' ' cm deg/s2 5 (3,9 = +/- 0.1 cm/sz 5 (ayi) = +/- 3.1cm/s2 5 (azi) = +/- 4.9 cm/s2 48 Estimated Percent Error The following example estimates the linear x and angular xy accelerations of a rower’s right shank. Martin and Bernfield (1980) found that the leg drive for elite male rowers took 0.67 seconds. The shank rotates approximately 90 degrees in the xy plane during the leg drive phase and will travel a distance of approximately 50 cm along the x axis. If constant acceleration is assumed, the linear and angular acceleration of a rower’s right shank can be estimated by the following calculations: 0f= 60 + (not + l/20t,‘y t2 and xf = x, + vot + 1/2 axt2 where 9°, (0,, x,- and v0 = O. or,y 2 2(90 deg)/(0.67s)2 = 400.98 deg/s2 +/— 4.2 deg/ $2 and a, = 2(50cm)/(0.67s)2 = 222.77 cm/52 +/- 0.1 cm/sz. Therefore, the percent error in calculating or,y = 100% * 8.4deg/sz/ 400.98 deg/s2 = 2.1% and in calculating ax = 100% * 0.2 cm/s2 / 222.77 cm/s2 = 0.09% Further Testing on the Uncertaing Coefficient The present study showed that the uncertainty depends largely on the angle between the cameras and the field of view. Proper triangulation (>60 degrees) between the cameras and the field of view may change the uncertainty coefficient. A follow-up study on the affects of yz camera rotation on digitized data needs to be completed before any kinematic testing of rowers takes place. Conchgigns The MVP in its present state is not accurate enough for use in an acceptable kinematic analysis of the rowing cycle. However, this study provided the basis for establishing a better tool in studying the kinematics of rowing. The equations established 49 in the laboratory allows for an approximation of the uncertainty in calculated x,y and -z coordinates when rotation and movement in the cameras occurs. By attaching the cameras to the shell rather than towing them, the effect on the uncertainty of digitized data is greatly reduced. However, further testing of the uncertainty coefficient is necessary because of the change in angle between the cameras and the field of view. 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0.005 ..0.1 0.11 ..500 ..001 0.11 0.000 0.0.. 0.01 0.010 0.0.. 1.01 0.100 .50.. 10 5.100 0.0. 0.500 0.001 5.01 0. .00 0. .01 0.01 1.0.0 0.1.. 1.01 1.010 5.0.. 5.01 5.500 100.. 00 1.000 0.1. 0.000 0.001 0.01 ..101 ..001 ..01 0.0 .0 0.0 .. ..01 0.000 0.... 0.01 0.000 500. . 00 0.000 0.0. 0.000 1.0.1 0.01 0.001 0.001 5.01 0.000 0.0.. 0.01 0.000 0.0.. 0.01 0.010 00.. .0 0.100 0.1. 0.050 5.0.1 0.11 1.551 0.001 ..01 ..501 0.0.. 1.51 0.0.0 0.1.. 0.51 ..000 000.. 00 1.000 ..1. 0.000 5.5 .1 0.11 0. .51 0.0.1 0.01 0. .01 0.... 0.51 1.0.0 1.0 .. 0.51 1.000 00.0 00 0.000 0.1. ..500 0.0.1 0.01 5.101 ..5 .1 0.01 1.001 0.0.. 0.51 0.000 0.0.. 0.01 0. .00 000.0 00 0.000 0.0. 0.010 0.5.1 0.11 0.501 0.5.1 0.11 0.151 0.0 .. 1.51 0.001 0.0.. 0.51 0.1.0 000.0 50 0. .00 0.1. 0.010 0.0.1 0.01 0.011 0.0.1 0.11 0.001 0.0.. ..51 0.001 1.00. 1.51 0.000 000.0 00 0.000 ..1. 0.000 0.0.1 1.11 0.011 0.0.1 5.11 0.001 0.0.. 0.51 0.001 .. . .. 0.01 1.81 0.0.0 00 0. .00 0.1. 0.100 0.1 .1 5.01 0. .01 0.0.1 0.01 0.011 0.00. 0.01 ..051 0.0.. 0.01 5.001 .00.0 10 ..000 ..1. 0.0.0 0.0.1 5.11 0.001 ..0 .1 0.01 0.011 0.00. 0.51 1.001 0.0.. 0.51 0.81 100.0 00 0. .00 0.0. 0.000 5.0 .1 0.01 ..0 .1 0.1.1 0.01 0.001 0.8. 1.01 0.001 0.8. 5.01 0.051 58.0 00 1.100 1.0. 0.500 ..1.1 1.01 0.001 0.0.1 0.01 0.101 0.8. 0.51 5.011 ..0.. 0.01 0.001 00.0 .0 0. .00 5.1. 5.000 0.0 .1 0.01 0.500 1.1.1 0.01 0.0.1 0.8. 0.01 0.001 0.50. 0.01 ..001 000.0 00 0.000 0.0. 0.000 0.0.1 0.01 0.000 0.0.1 0.11 0.501 0.00. 0.01 1.001 0.0.. 1.01 5.111 0.0.0 01 0.000 0.0. 0. .50 0.001 0.01 0.050 0.0.1 0.01 5.80 0.50. 0.11 0.0.1 0.00. 1.01 0.001 005.0 01 0. .00 0.1. 0.000 0.001 0.01 0.050 0. . .1 0.01 0.000 0.00. 5.11 0.0.1 0.50. 0.01 0.501 005.0 51 APPENDIX B Digitizing Error gn Movements of the MVP 59 I Digitizing qucm) 7m: 1 anqo.917s) dx dy dz I911 0: fly dz I911 1 19.9 9.4 9.9 17.9 19.4 9.1 9.9 19.9 2 19.9 9.9 2.2 19.9 19.9 9.9 2.9 19.2 9 19.1 9.4 9.1 19.9 17.9 9.9 4.1 19.9 4 19.9 9.4 2.1 19.7 19.7 9.9 9.7 19.9 9 14.9 9.9 1.9 14.7 17.9 9.4 9.4 19.9 9 19.2 9.9 22 19.9 19.9 9.9 9.2 19.9 7 19.7 9.9 9.9 17.9 19.1 9.2 9.4 19.4 9 19.9 9.9 4.7 19.9 19.9 9.4 4.9 19.9 9 19.9 94 9.2 19.9 17.9 9.2 1.9 17.9 19 19.9 9.2 9.2 17.2 17.4 9.9 4.9 19.9 11 19.9 9.9 1.7 19.9 19.9 9.9 29 19.9 12 19.9 9.2 2.9 17.1 17.9 9.9 '12 17.9 19 192 94 2.7 19.4 172 9.9 1.7 17.9 14 19.9 9.9 9.9 19.9 17.1 9.1 9.2 17.4 19 19.9 9.2 2.9 19.9 19.9 9.2 4.9 19.9 19 19.2 9.9 29 19.9 19.9 92 9.9 19.9 17 19.9 9.9 -9.9 19.9 19.2 -9.1 .14 19.9 19 19.9 9.9 9.9 19.9 172 9.1 1.9 17.9 19 19.9 9.9 9.7 19.9 19.9 9.9 1.9 19.1 29 19.9 9.1 9.1 19.9 194 9.9 9.9 194 21 19.1 9.1 -9.4 19.1 19.9 92 21 19.9 22 19.9 9.1 -9.9 19.9 19.9 9.1 1.4 19.1 29 19.9 9.1 9.1 19.9 194 9.9 2.1 19.9 24 19.1 92 -1.9 19.1 19.7 9.7 9.9 19.1 29 19.9 9.2 9.7 19.9 19.7 94 2.9 19.9 29 19.4 9.2 2.9 19.9 19.1 9.1 2.9 19.2 27 19.7 9.9 9.9 19.7 19.9 9.1 1.7 199 29 19.7 94 2.4 19.9 19.9 94 9.9 192 29 19.9 9.1 92 19.9 17.1 9.1 1.4 172 99 192 9.1 1.9 19.9 194 9.9 2.9 19.9 91 19.7 -9.1 -9.9 19.7 19.9 9.9 4.9 19.9 92 19.9 94 1.9 199 19.9 9.9 2.9 19.1 99 19.9 9.2 9.9 19.9 19.9 9.1 -9.1 199 94 19.1 92 9.4 19.1 17.9 9.9 12 17.9 99 19.9 94 14 19.7 194 9.9 1.9 19.9 99 19.9 92 1.9 19.9 19.9 94 2.9 17.1 97 19.7 94 1.9 19.9 17.9 9.4 2.7 19.1 99 194 9.9 2.9 19.9 17.1 9.9 9.7 17.1 99 14.9 9.9 1.9 14.9 19.7 92 9.2 17.9 49 19.9 92 9.9 19.9 17.9 92 9.4 17.9 41 19.9 9.9 9.9 19.9 17.9 9.7 2.9 17.9 42 19.9 9.4 2.9 19.1 17.9 94 1.9 17.7 49 19.9 -9.9 -9.9 19.9 19.7 9.9 14 19.9 44 17.9 9.4 2.9 17.7 19.9 -9.1 9.9 19.9 49 19.9 9.9 1.9 19.9 19.9 92 9.9 19.9 49 17.7 9.1 1.9 17.9 19.4 92 1.9 194 47 17.9 92 9.9 17.9 19.9 94 22 19.9 49 17.9 9.0 0.9 17.9 19.2 9.9 1.1 19.9 49 17.0 0.0 9.4 17.0 19.0 0.4 0.9 19.0 90 19.9 9.1 0.1 19.0 19.9 0.1 -9.9 19.9 91 19.9 9.1 -0.7 19.9 17.4 9.4 9.1 17.4 92 19.9 0.9 1.7 19.1 19.2 0.0 -9.4 19.2 99 19.9 0.9 0.1 19.9 17.9 92 -0.9 17.9 94 19.9 0.9 0.9 19.9 19.9 9.9 .12 19.9 99 19.9 9.2 0.9 19.9 19.9 0.1 -2.9 19.7 99 19.9 9.0 0.7 19.9 19.9 -0.1 -2.1 19.4 97 19.9 9.4 1.9 19.9 19.0 9.1 -9.9 19.1 99 19.4 9.4 0.1 19.4 17.4 0.9 0.9 174 99 19.0 0.9 -0.9 19.9 19.1 9.0 1.9 19.2 90 19.9 9.2 1.7 19.7 17.7 9.9 1.0 17.9 91 19.9 9.2 0.7 19.9 17.9 0.1 -0.9 17.9 92 19.1 0.1 9.7 19.1 19.9 94 1.7 19.1 99 19.2 0.2 -9.9 19.2 19.9 0.1 -9.9 19.9 94 19.9 0.9 0.2 19.9 19.9 0.2 -0.9 19.0 I Maximum 17.9 0.9 9.1 17.9 19.4 I 9.9 9.2 19.9 Mlnimum 14.6 16.5 Dlfloronco 3.2 3.1 Digitizing Errortcm) Trial 2 [Fr-19.19.0179) dx dy 0: 1911 dx 0y dz 1911 1 19.0 .02 9.2 19.4 199 0.1 9.9 17.9 2 19.7 9.9 -9.7 19.7 19.9 0.0 .94 19.9 9 17.9 9.9 .27 19.9 19.2 92 -0.4 192 4 19.9 9.0 9.9 19.9 19.9 0.9 -1.9 19.7 9 19.7 -9.1 .99 17.2 17.9 0.1 -1.9 17.9 9 144 9.1 -1.9 14.9 19.1 04 .14 192 7 19.9 9.9 -0.9 19.9 17.9 0.1 -1.9 17.9 9 19.9 92 -9.1 19.9 19.7 0.2 .92 19.9 9 19.9 9.9 -0.7 19.9 19.9 9.1 94 19.9 19 17.9 9.0 .92 17.9 19.9 0.9 9.9 19.9 11 19.7 0.1 -1.9 19.9 19.9 02 -1.9 19.9 12 17.1 0.1 .94 174 19.9 9.0 .27 19.7 19 19.0 9.1 9.1 19.0 19.1 9.9 -2.1 192 14 19.9 0.9 1.9 19.9 19.4 0.2 -9.9 19.4 19 17.9 9.2 -1.9 17.9 19.1 0.9 -94 19.1 19 19.9 0.9 .12 19.9 19.9 02 .1.9 19.7 17 17.9 0.2 -0.9 17.9 19.1 9.2 -0.9 19.1 19 19.9 02 0.9 19.9 17.9 92 0.1 17.9 19 17.9 9.1 -9.1 17.9 19.2 -0.1 22 19.9 20 19.4 0.9 -2.9 19.9 17.7 0.2 -9.9 17.7 21 172 9.9 -0.9 172 17.7 92 -1.9 17.9 22 17.1 0.2 -14 172 17.9 -9.1 .1.9 17.9 29 17.7 9.9 12 17.9 17.7 0.9 -9.9 17.7 24 17.9 02 1.7 17.9 19.9 9.9 -0.9 19.9 29 192 9.2 .21 19.9 19.9 9.9 1.9 19.7 29 19.9 9.7 1.1 19.9 19.9 0.9 -9.9 19.9 27 17.0 0.1 -9.9 17.0 17.9 9.9 .92 19.2 61 28 18.0 0.1 1.8 18.1 18.5 0.1 -0.6 18.5 29 18.6 0.4 0.8 18.6 19.1 0.6 1.2 19.2 30 18.5 0.3 1.3 16.6 17.4 0.2 0.3 17.4 31 16.4 0.2 -0.4 16.4 18.6 0.3 0.5 1 8.6 32 16.9 0.2 -0.3 16.9 18.2 0.1 -1.0 18.2 33 16.2 0.3 2.0 16.4 1 8.9 0.2 -0.4 18.9 34 17.4 0.3 0.0 17.4 18.7 0.5 1.8 18.8 35 17.2 0.4 1 .4 17.3 19.7 0.4 3.0 20.0 36 16.6 0.2 2.1 16.7 1 8.8 0.3 0.5 18.6 37 17.1 0.1 0.7 17.1 19.2 0.3 -1.4 19.3 38 17.3 0.1 0.1 17.3 1 6.9 0.2 -0.8 16.9 39 18.2 0.4 0.7 18.2 17.4 0.0 0.0 17.4 40 17.5 0.3 2.0 17.6 18.5 0.4 1 .1 18.5 41 17.3 0.5 2.0 17.4 18.8 0.4 1 .5 18.9 42 17.3 0.4 0.8 17.3 19.3 0.2 0.3 19.3 43 18.4 0.3 -1.0 16.4 1 8.7 0.3 -1.0 1 8.7 44 17.3 0.4 3.2 17.6 18.1 0.2 -0.8 18.1 45 17.3 0.1 0.7 17.4 1 9.0 0.2 0.1 19.0 48 17.2 0.2 0.5 17.2 18.9 0.3 -0.7 18.9 47 16.1 0.3 2.2 16.2 19.2 0.4 0.5 19.2 48 15.9 0.3 3.6 1 6.3 1 8.5 0.3 0.2 18.5 49 17.3 0.3 2.1 17.4 20.7 0.3 -1.8 20.8 50 17.1 0.5 1 .3 17.1 1 8.8 0.5 0.6 18.8 51 16.2 0.4 3.2 18.5 18.7 0.2 0.4 18.7 52 16.2 0.4 4.9 17.0 1 7.1 0.2 -0.9 17.1 53 24.6 0.2 7.0 25.8 20.2 0.5 2.0 20.3 54 31 .9 0.3 6.4 32.6 19.2 0.4 2.0 19.3 55 16.4 0.3 0.0 18.4 1 9.0 0.2 1 .6 19.1 56 16.8 0.4 0.2 16.8 20.1 0.3 0.9 20.1 57 17.7 0.3 0.3 17.7 20.0 0.4 2.4 20.1 58 18.0 0.2 0.4 18.0 1 8.3 0.3 0.3 1 8.4 59 17.3 0.2 -0.9 17.3 1 9.2 0.3 1.1 19.3 80 17.6 0.4 3.3 17.9 1 9.0 0.6 2.3 19.2 81 17.6 0.6 2.7 1 7.8 18.5 0.4 0.2 18.5 62 17.0 0.3 2.8 17.2 19.3 0.3 0.6 19.3 63 1 8.2 0.4 -0.6 1 8.3 1 8.6 0.5 1 .9 18.7 64 18.3 0.5 2.3 18.5 19.1 0.3 0.4 19.1 85 17.4 0.3 1 .9 1 7.5 1 9.0 0.5 1 .0 1 9.0 86 17.7 0.3 3.7 18.1 19.0 0.7 0.4 19.0 87 17.0 0.6 2.2 17.1 1 8.9 0.3 2.6 1 9.1 68 16.3 0.2 0.7 16.3 18.7 0.4 1.5 18.7 89 17.1 0.3 3.5 17.5 18.2 0.3 0.5 18.2 70 18.2 0.1 4.7 18.8 20.8 0.4 4.0 21 .2 71 18.1 0.2 3.7 18.5 18.9 0.4 0.2 18.9 72 17.0 0.4 2.9 17.2 18.8 0.3 1 .6 1 8.9 73 17.7 0.3 4.0 1 8.1 18.5 0.3 0.4 1 8.5 74 18.5 0.5 3.9 18.9 18.3 0.3 1 .6 18.4 62 Minimum 14.4 -0.2 -5.7 14.5 16.9 -0.1 -3.4 16.9 17.5 0.9 12.6 18.1 3.9 0.8 7.5 4.3 019102an Errortcm) Trial 5 Era-9.19.9179) dx dy dz 1911 dx dy dz Ion 1 18.6 0.2 1.6 22.5 20.8 0.0 2.4 21.0 2 16.3 0.1 1.6 21.3 21.7 0.4 4.4 22.2 3 16.6 0.1 3.8 22.6 20.3 0.5 5.9 21.1 4 17.4 0.6 4.1 21 .8 ”.3 0.5 6.3 21 .2 5 18.7 0.1 3.1 22.5 18.6 0.7 4.6 19.2 8 17.0 0.4 3.4 21 .9 19.3 0.5 4.3 19.8 7 17.2 0.3 3.5 23.3 18.2 0.5 3.5 18.5 8 16.8 0.3 3.9 24.2 19.3 0.2 4.0 19.7 9 16.7 0.5 4.4 24.3 18.0 0.3 2.7 1 8.2 10 18.1 0.2 2.4 23.3 1 9.0 0.5 3.3 1 9.3 11 15.4 0.0 2.1 23.2 18.9 0.3 2.7 1 9.1 12 15.8 0.1 2.1 23.1 18.6 0.3 4.0 19.0 13 15.4 0.1 1.7 22.4 16.8 0.5 4.0 ”.2 14 15.8 0.4 4.8 22.1 19.5 0.5 3.6 19.8 15 15.8 0.4 5.0 22.9 1 8.6 0.4 3.5 18.9 18 18.6 0.3 1.7 21 .3 18.9 0.5 4.5 19.4 17 17.2 0.4 2.7 21 .1 19.2 0.4 4.4 19.7 1 8 16.9 0.2 2.0 22.2 18.3 0.2 2.3 18.5 19 18.3 0.3 1 .9 22.2 18.4 0.4 2.8 1 8.7 20 17.5 0.1 1.4 21.3 10.0 0.5 1.3 18.1 21 18.0 0.2 1 .7 ”.9 ”.0 0.8 3.8 20.4 22 17.2 0.3 2.3 20.5 19.8 0.8 2.7 ”.0 23 17.4 0.3 2.4 21 .3 18.1 0.5 4.3 18.6 24 16.1 0.2 1.0 ”.6 19.1 0.4 3.2 19.4 25 16.5 0.2 3.7 21.1 19.1 0.4 2.5 19.3 26 16.8 0.3 2.5 21.7 18.8 0.3 2.7 18.1 27 16.2 0.3 1 .9 22.1 19.1 0.4 3.3 1 9.4 28 16.9 0.2 2.2 21 .9 1 7.0 0.1 3.0 17.2 29 16.5 0.4 1 .8 21 .5 19.2 0.3 3.9 19.6 30 16.5 0.2 2.0 ”.8 18.9 0.7 3.7 ”.3 31 15.9 0.1 1 .1 ”.3 19.2 0.8 4.3 1 9.7 32 15.3 0.2 0.4 21.8 17.5 0.5 3.3 17.6 33 16.1 0.3 0.7 21.1 17.9 0.4 3.3 18.2 34 16.1 0.4 1 .0 ”.9 17.7 0.4 2.9 1 7.8 35 15.8 0.1 1.1 21.0 16.6 0.3 3.4 16.8 36 15.2 0.0 1.3 21.6 16.4 0.4 2.5 16.6 37 15.6 0.1 1.0 18.6 16.8 0.5 3.0 19.2 99 17.0 0.4 2.6 ”.1 17.0 0.3 2.3 1 7.1 39 14.8 0.0 0.2 21 .2 1 8.5 0.4 1 .8 1 8.6 40 14.5 0.3 0.6 21 .7 1 8.0 0.3 1 .2 1 8.0 41 14.4 0.1 0.8 ”.5 17.8 0.0 1.7 1 7.9 42 16.0 0.0 1.2 18.9 16.0 0.5 3.3 18.3 43 15.7 0.0 1.6 ”.5 16.3 0.0 0.3 16.3 44 15.6 0.0 0.4 19.5 18.1 0.3 0.1 16.1 45 16.3 0.1 1.6 19.7 16.3 0.3 2.1 16.4 63 46 15.7 0.0 0.9 19.9 17.9 0.3 2.2 18.0 47 16.6 0.0 1.0 17.9 18.0 0.3 1.5 18.1 48 16.3 0.1 1.5 18.0 18.3 0.2 1.1 18.4 49 15.6 0.0 -0.6 19.2 17.8 -0.2 0.6 17.8 80 16.3 0.3 1.6 18.9 18.2 0.2 1.3 18.2 51 16.0 0.4 0.6 18.8 18.7 0.3 1.2 1 8.8 52 14.7 0.2 1.5 18.2 18.6 -0.1 0.7 18.6 83 16.4 -0.1 1.4 17.5 16.9 0.1 1.3 18.9 54 1 5.2 0.1 -0.4 1 8.3 18.5 0.2 1.8 18.6 58 15.9 0.2 0.9 18.5 17.1 0.2 0.9 17.1 58 1 5.8 0.2 0.8 18.2 17.6 «0.2 -0.2 17.6 87 16.1 0.1 -0.1 17.7 17.5 «0.1 -0.9 17.5 58 1 5.4 0.0 1 .8 17.9 17.8 0.3 2.2 17.7 59 1 5.1 0.2 0.1 17.9 17.2 0.1 0.2 1 7.2 60 15.4 -0.1 «0.4 17.4 17.8 0.3 0.6 17.8 61 1 8.9 -0.3 -1 .2 1 7.3 17.7 0.3 1 .3 17.8 62 1 5.8 -0.1 -1.0 1 6.6 19.2 0.1 3.2 19.5 63 1 5.8 0.0 1.1 17.7 17.8 0.3 1.9 17.7 64 1 6.1 0.2 1.0 16.7 17.8 0.2 0.6 17.8 68 14.9 «0.1 0.0 17.8 18.2 «0.1 0.8 18.2 66 1 8.0 0.0 0.2 1 7.7 17.3 0.3 1.1 1 7.4 67 16.0 0.2 «0.1 16.4 16.6 0.3 0.4 16.8 66 15.1 0.0 -0.2 16.6 16.3 0.1 0.6 16.3 68 15.3 0.0 0.0 16.5 16.5 0.2 0.5 16.5 70 15.7 0.1 «0.5 17.2 17.2 0.1 .04 17.2 Maximum 1 8.6 0.6 5.0 24.3 21 .7 0.8 6.3 22.2 Minimum Digiflzlng Erratum) Emomn) dx dy 0: i911 1191 dy 9: 1911 I 1 19.9 9.9 2.9 29.7 19.9 9.4 2.7 19.7 2 14.9 9.4 9.9 21.1 19.1 9.7 9.9 19.9 3 16.1 0.4 2.5 20.3 17.1 0.7 2.2 17.2 4 19.9 9.9 9.7 21.2 19.9 9.9 4.9 174 5 18.1 0.4 1.5 20.8 17.8 0.8 3.3 17.9 8 14.1 0.3 2.4 20.4 17.8 0.4 2.1 17.8 7 14.9 9.9 22 19.9 192 9.9 1.9 19.9 9 194 9.9 2.9 29.9 172 0.9 9.1 174 9 19.9 9.9 2.2 19.1 17.9 9.9 9.9 19.9 10 1 5.4 0.7 2.4 17.9 1 8.2 0.5 3.5 18.8 11 19.9 9.9 1.1 19.9 17.9 9.9 4.1 19.2 12 19.9 9.9 1.9 19.7 19.9 9.9 4.9 19.9 19 19.9 9.4 1.9 19.9 17.7 9.9 9.9 19.1 14 19.9 9.3 1.1 19.9 11.9 9.9 1.7 19.9 15 14.5 0.8 2.4 19.9 17.4 0.8 3.3 17.8 18 18.8 0.2 2.4 19.8 17.2 0.5 3.7 17.8 1 7 16.1 0.5 3.6 18.6 17.8 0.6 1.4 17.9 19 19.9 9.9 9.9 19.9 17.9 9.9 2.9 17.9 19 14.9 92 9.1 29.9 194 9.7 9.9 19.9 64 20 14.1 0.4 0.4 21.3 17.6 0.4 2.1 17.8 21 15.8 0.1 0.2 20.5 18.1 0.6 1.6 18.2 ” 14.6 0.1 0.2 20.4 17.3 0.4 3.5 17.6 23 15.7 0.5 2.5 20.0 17.1 0.8 3.1 17.4 24 15.7 0.4 4.0 19.5 18.4 0.6 2.8 1 8.6 25 16.0 0.4 0.6 18.8 17.9 0.6 3.4 18.2 28 14.7 0.4 0.9 18.8 19.0 0.6 5.1 19.7 27 18.0 0.5 0.2 1 9.9 17.4 0.8 4.5 1 8.0 28 15.5 0.4 -0.5 1 9.5 17.5 0.7 4.3 1 8.1 29 16.3 0.2 0.7 19.8 18.1 0.8 1 .3 18.1 30 18.5 0.2 -1.1 18.5 18.2 0.8 3.7 18.6 31 15.3 0.2 0.9 18.3 18.4 0.3 2.5 18.6 32 15.6 0.3 1.4 19.2 1 8.5 0.8 3.1 18.7 33 15.1 0.7 3.2 21.3 16.9 0.3 1.1 17.0 34 14.8 0.5 2.6 19.7 18.6 1 .0 4.8 1 9.3 35 15.9 0.8 2.8 20.1 17.8 0.5 1.4 17.8 36 15.1 0.4 0.8 20.4 17.8 0.6 4.2 18.3 37 15.5 0.5 1.8 20.4 18.4 0.6 3.7 18.7 38 18.5 0.4 1.3 ”.2 1 7.5 0.3 2.1 17.6 39 16.4 0.6 0.9 19.9 17.9 0.8 0.2 17.9 40 15.9 0.8 1 .8 20.8 18.3 0.5 2.4 18.5 41 18.9 0.4 0.1 21.6 17.5 0.2 2.5 17.7 42 15.7 0.4 1 .3 ”.3 18.0 0.4 2.5 1 8.1 43 1 8.4 0.2 -0.9 21 .9 1 7.6 0.7 1 .3 17.7 44 15.1 0.2 0.3 22.5 17.5 0.8 1.5 17.8 45 14.1 0.4 2.1 22.4 18.4 0.4 2.0 18.5 46 15.8 0.1 «0.7 21.5 18.5 0.7 3.1 18.8 47 14.7 0.3 0.7 ”.0 18.3 0.4 1 .8 18.4 48 1 6.1 0.5 1.4 21.1 19.2 0.6 3.1 1 9.5 49 18.3 0.5 1.5 21.1 17.8 0.5 1 .1 17.8 50 15.5 0.2 «0.9 20.2 18.5 0.7 1.5 18.5 51 16.3 0.3 1.4 ”.5 17.4 0.4 0.9 17.5 52 14.7 0.4 0.1 23.4 1 7.7 0.4 1 .6 1 7.7 53 14.8 0.4 0.1 22.8 19.4 0.8 2.2 1 9.5 54 1 6.6 0.3 0.9 23.5 1 8.4 0.6 1 .6 1 8.5 55 1 8.1 0.1 0.2 24.3 1 7.7 0.3 1 .2 17.7 58 15.1 0.4 -0.6 24.1 17.8 0.4 1 .0 17.8 57 14.9 0.5 ‘0.1 25.3 17.1 0.5 0.1 17.1 58 18.4 0.4 2.2 23.2 17.6 0.6 0.8 17.7 59 17.0 0.3 -1.2 21 .1 19.4 0.6 0.6 19.5 80 1 8.9 0.5 1 .8 ”.1 1 9.7 0.8 1 .3 1 9.7 61 18.0 0.5 0.3 21.9 19.8 0.2 1.4 19.5 62 1 5.0 0.5 -1 .4 23.0 17.9 0.1 -0.5 17.9 63 15.3 0.3 -0.9 23.0 17.7 0.2 0.7 17.7 64 1 6.5 0.5 0.0 ”.8 18.4 0.3 1 .0 18.4 65 1 5.9 0.2 -0.8 23.1 18.4 0.3 1 .9 1 8.5 66 18.3 0.1 -2.9 21 .3 18.2 0.8 2.1 18.4 67 1 6.3 0.6 0.7 23.5 18.1 0.4 0.7 18.1 68 18.1 0.4 1 .0 ”.4 18.7 0.5 0.7 18.7 65 69 15.0 0.2 -0.7 23.0 18.5 0.5 0.7 18.5 70 15.2 0.2 -1.0 23.2 16.6 0.3 1.3 18.6 71 16.9 0.2 0.0 22.7 18.8 0.5 1.1 16.8 72 17.4 0.2 0.0 23.3 20.3 0.3 -2.9 20.5 73 17.7 0.4 -1.6 23.9 19.4 0.5 -1.3 19.5 74 18.6 0.5 0.1 21.2 19.6 0.4 -1.0 19.6 75 15.1 0.3 -0.9 23.5 19.6 0.8 0.4 19.6 76 16.3 0.1 -0.8 23.2 18.5 0.4 -0.8 18.5 I Maximum 18.6 0.7 4.0 25.3 20.3 1.0 5.9 20.5 Minimum 0.1 -2.9 17.0 0.9 i 8.8 1 3.5 ' APPENDIX C Calculations of x axis movements of the Mobile Video Platform 66 ane(0.0179) X(9h9ili- 111111109919) 1 -71.0 127.4 161.2 2 41.1 -63.7 97.8 128.9 161.5 3 -25.8 -59.4 103.3 129.1 162.7 4 -17.3 -81.0 111.1 128.5 162.1 5 -10.1 43.5 119.2 129.3 162.7 6 4.7 47.4 124.8 128.5 162.3 7 2.3 432.0 129.5 127.2 161 .5 8 7.8 -25.7 136.7 128.9 162.4 9 14.2 .21 .0 141 .9 127.7 162.9 10 Catch 19.2 ~14.2 148.6 1”.5 162.8 11 27.8 -8.9 158.1 127.4 162.0 12 31 .8 -2.7 1 80.8 128.6 183.2 13 38.2 3.2 186.2 128.0 1Q.1 14 42.0 7.4 1 70.4 128.3 163.0 15 47.2 14.0 176.3 129.0 162.3 1 6 82.3 19.2 1”.9 128.6 161.8 17 59.4 25.4 1”.3 128.9 162.9 18 64.6 29.3 192.8 1 28.2 163.8 19 89.3 35.5 1”.0 128.7 182.5 ” 75.1 41 .1 ”4.3 1 29.2 1 63.2 21 81 .5 47.7 21 0.5 1 ”.0 1 62.7 22 87.4 54.0 21 7.6 130.2 183.6 23 92.3 58.7 ”2.7 130.4 184.0 24 ”.2 84.7 ”8.8 1 30.6 1 84.1 25 103.7 71.4 234.5 1”.8 163.1 26 11 0.3 76.6 240.9 130.5 184.3 27 1 17.3 81 .9 246.7 1 ”.4 1 64.8 28 1 23.9 90.3 253.9 130.0 163.7 29 129.1 ”.0 280.8 131 .7 188.8 30 135.0 101.7 264.9 129.9 183.2 31 141 .8 109.1 271.4 1 ”.6 1 62.3 32 End L69 DINO 147.5 114.5 278.3 1 ”.8 183.8 33 153.8 1 21 .6 284.0 130.3 182.4 34 1”.4 128.2 2”) 130.3 1 62.5 35 167.8 134.4 2”.3 130.5 183.9 38 176.5 141 .8 ”4.3 127.8 182.7 37 181 .0 147.6 31 0.9 1”.9 163.3 38 - 187.8 1 54.4 31 7.2 1”.8 1 82.8 39 1 94.4 1 61 .9 325.9 1 31 .5 1 84.0 40 201 .0 168.0 331.4 130.4 183.4 41 ”.1 1 75.7 339.7 1 31 .6 184.0 42 213.8 181 .7 348.0 132.2 164.4 43 ”1 .8 189.7 353.2 131 .4 1 83.4 44 230.2 196.8 361 .0 1 ”.8 164.2 45 238.2 203.2 388.4 1 30.3 1 63.3 46 248.0 211.9 378.7 1&1 183.9 47 252.5 21 9.8 3”.6 1 28.1 1 61 .0 67 48 259.2 225.4 389.7 130.6 164.3 48 266.2 232.8 384.9 128.7 162.1 50 273.3 240.6 404.2 130.8 163.5 51 280.9 248.2 412.4 131.5 164.2 52 288.3 255.6 419.2 130.8 1 63.6 53 295.4 263.2 427.2 131.8 164.0 54 Finish 302.7 270.7 434.1 131.4 163.4 55 309.6 278.9 443.0 133.3 164.1 56 318.0 287.0 450.3 131.3 163.3 57 326.5 284.0 457.2 130.7 163.3 58 333.2 300.6 464.8 131.6 164.2 58 338.8 308.3 472.8 133.0 164.6 60 347.7 315.6 480.0 132.3 164.4 61 355.2 322.5 488.0 132.8 165.5 62 364.0 331.1 486.3 132.3 165.2 63 371.5 338.4 504.0 132.5 164.6 64 378.4 346.8 510.2 130.8 163.4 74991 133.3 165.8 “in 127.2 161.0 OM «6.1 -4.8 Calculation of X-axis movements(cm) Trial 2 111911911)- X(9l19ll)- 919199109179) Evan! X(lflncam) X(rtmcam) X(shoil) 1111111110919) 4781169111) 1 67.8 47.7 ”6.3 138.5 158.6 2 76.8 55.7 213.6 136.6 157.8 3 63.2 62.6 220.1 136.8 157.5 4 68.7 68.8 227.5 187.8 157.6 5 ”.0 77.4 235.4 137.4 188.0 6 103.1 83.5 240.8 137.7 157.3 7 112.2 80.3 248.7 137.5 158.4 8 118.4 87.8 256.7 137.3 158.8 8 127.0 1N0 284.7 137.7 158.7 10 Finish 132.8 111 .6 288.8 137.0 158.3 11 141.0 118.0 278.1 137.1 158.1 12 147.8 125.5 284.7 136.8 168.2 13 155.3 132.6 282.4 137.1 158.8 14 162.6 140.8 288.8 137.3 158.0 15 171.2 147.8 30.4 137.2 180.7 16 176.1 154.8 314.4 136.2 158.4 17 15.0 162.2 9221 137.1 158.8 18 181.6 168.2 326.8 137.4 158.7 18 188.1 176.5 336.6 137.5 1N.1 20 ”6.1 163.0 343.1 137.0 160.1 21 213.3 180.8 350.5 137.2 158.7 22 ”0.5 187.4 357.7 137.2 160.3 23 228.7 207.1 367.4 137.7 1N4 24 238.8 214.5 374.1 135.2 158.6 25 245.1 222.6 362.0 136.8 158.4 26 253.1 231 .0 380.5 137.4 158.6 68 27 261.1 238.0 388.2 137.1 160.2 28 268.8 245.5 406.6 137.7 161.1 28 276.7 253.5 413.3 136.6 158.8 30 369 8681 M081 284.2 260.8 422.3 138.1 181.3 31 283.0 268.3 430.3 137.2 161.0 32 300.7 277.5 437.8 1 37.1 160.4 33 308.2 285.0 448.8 138.5 161.8 34 316.8 283.1 454.8 138.1 161.7 35 326.7 303.2 464.5 137.8 161.3 38 333.2 308.7 471.6 138.4 162.0 37 341.6 317.8 478.6 138.0 181.8 38 350.8 326.3 488.4 1 38.5 163.1 38 358.6 333.8 485.8 1 37.3 162.0 40 368.7 342.1 504.8 138.2 182.8 41 375.7 352.0 513.8 138.1 161 .8 42 383.4 358.2 521 .4 138.0 162.2 43 383.1 367.8 531.3 1 38.2 163.5 44 400.4 375.8 538.1 1 37.6 1 62.3 45 «.8 384.1 547.4 138.5 183.3 48 41 6.8 382.2 554.7 1 37.8 1 82.5 47 425.1 401.8 564.0 1 38.8 182.2 48 432.7 408.4 572.0 138.4 182.6 48 442.8 417.5 578.3 136.4 181.8 50 448.8 424.8 587.5 137.6 162.8 51 457.8 433.3 ”.0 140.2 184.6 52 465.4 440.1 803.1 137.7 162.8 53 473.8 448.2 61 3.6 138.8 164.3 54 481 .1 454.8 81 7.5 136.4 182.7 55 487.8 463.6 625.5 137.6 181.8 58 485.7 471.1 633.0 1 37.4 181.8 57 503.0 478.0 641 .0 1 38.1 163.1 58 508.8 483.8 846.8 137.1 163.0 58 515.7 481 .1 652.0 1 36.4 161 .0 80 523.1 “.0 661 .2 138.1 163.2 81 530.2 504.5 887.8 137.8 163.3 82 536.2 51 1 .2 674.0 137.8 1 m 63 542.0 517.0 8N1 138.2 163.2 84 548.3 523.8 “7.5 1 38.2 183.6 65 555.1 528.8 683.3 1 38.3 163.4 86 081011 558.8 535.5 ”.3 138.5 182.8 67 567.2 542.2 704.8 1 37.8 162.7 88 571.7 547.1 710.5 1 38.7 183.4 68 577.1 551.1 716.3 138.2 165.2 70 584.4 558.6 721.6 1 37.2 182.0 71 588.3 582.8 726.3 138.0 163.4 72 582.8 568.3 730.8 1 38.1 162.6 73 588.0 573.5 738.4 138.5 185.0 74 804.8 578.6 743.1 1 38.2 184.5 75 608.2 584.7 748.2 140.0 164.5 69 In 140.2 165.2 Min 1 35.2 157.3 Dill -5.0 -7.9 Calculation of X-axis movements(cm) Trial 5 when). mm). anolo.017s) Event X(itfrtcam) X(rflmm) X(sholi) xlitl‘rbcam) «mini 1 -30.7 -71.8 104.2 134.8 176.0 2 -21.5 -59.1 115.2 136.7 174.3 3 -13.4 -52.7 122.5 135.9 175.2 4 -4.4 -43.6 131.4 135.8 174.8 5 4.6 -34.4 139.7 134.9 174.1 6 11.9 -27.1 147.1 135.3 174.2 7 21.6 -18.0 155.7 134.2 174.7 6 30.8 -10.3 164.4 133.6 174.6 9 37.4 -3.6 170.6 133.2 174.2 10 Catch 46.0 6.6 179.6 133.6 173.0 11 53.2 14.5 186.4 133.2 171.8 12 59.2 20.3 183.7 134.6 173.4 13 66.2 28.3 200.8 134.7 172.6 14 74.0 36.1 208.0 134.1 171.8 15 78.6 40.8 212.6 133.0 171.7 16 87.3 48.3 220.8 133.5 171.5 17 83.5 55.2 225.8 132.4 170.7 18 100.5 61.4 232.8 132.3 171.4 18 105.5 66.8 238.2 132.7 171.3 20 112.4 73.6 245.0 132.6 171.4 21 118.1 78.2 248.3 131.2 170.1 22 124.3 86.5 257.3 133.0 170.8 23 130.5 81 .8 263.6 133.1 171.8 24 134.7 87.8 268.1 133.4 170.3 25 141.3 103.6 274.2 132.8 170.6 26 150.6 112.0 282.8 132.2 170.8 27 156.3 118.0 2'4 132.1 170.4 28 163.8 124.8 285.2 131.5 170.3 28 171.5 133.4 ”2.3 130.8 168.8 30 177.5 140.3 313.8 131.4 168.6 31 162.6 146.4 314.1 131.5 167.7 32 181.2 153.4 #3225 131.3 168.1 33 186.4 158.2 328.3 131.8 168.1 34 204.4 167.4 336.4 132.0 168.0 35 210.8 173.8 342.4 131.7 168.5 36 End 81 Log Dflw 218.2 181.4 348.6 131.6 168.4 37 224.0 188.1 357.0 132.4 167.9 38 233.8 188.7 364.8 131.0 168.2 39 236.8 202.8 371.2 132.5 166.5 40 247.0 210.8 378.7 131.6 167.8 41 253.4 216.5 386.1 132.7 167.6 42 263.5 227.7 384.6 131 .0 166.8 43 268.1 232.8 388.5 1 30.5 166.7 44 277.4 242.2 408.6 132.2 167.4 7O 45 284.6 248.6 415.7 131.1 167.1 46 292.3 256.7 423.8 131.5 167.0 47 300.4 265.8 431 .4 131.0 1 65.5 48 307.6 273.3 439.5 131.9 166.2 48 315.0 2&1 446.0 131.1 165.8 50 324.8 289.7 455.6 130.8 166.0 51 330.8 286.0 460.9 130.1 164.8 52 338.0 305.2 470.1 132.0 164.8 53 348.0 314.2 479.2 131.2 165.0 54 355.8 322.2 486.1 130.3 163.8 55 362.5 328.2 484.3 131.8 166.1 56 372.2 338.3 5028 130.5 164.5 57 378.4 345.6 508.8 130.4 164.1 56 367.6 354.3 518.5 130.8 164.2 56 395.2 362.2 526.6 131 .4 1 64.5 60 Finish 403.6 370.8 533.9 130.1 162.9 61 411.3 378.1 542.6 131.3 164.6 62 420.1 367.7 551.1 131.0 163.4 63 427.8 384.6 558.2 130.2 163.6 64 435.7 403.0 566.1 130.4 1 63.1 65 444.0 411.4 575.6 131.6 164.2 66 452.2 418.5 563.0 130.8 164.5 67 460.2 427.7 580.2 130.0 162.4 66 468.5 437.8 600.1 130.6 162.3 68 476.6 446.5 606.6 130.0 162.2 70 486.4 453.5 615.4 128.0 162.0 Max 1 36.7 176.0 I “in 128.0 162.0 Oil! -7.6 -14.0 I Ealcuiation of X-axis movements(cm) Trial 6 mm»)- um; | mmqom 7s) Event xmmm) X(mmln) X(shsli) “mm HM) 1 44.5 7.4 173.0 126.5 165.6 2 50.6 15.6 179.8 128.3 164.3 3 56.6 23.2 1N3 128.5 168.0 4 65.8 28.7 184.1 126.4 165.4 5 74.6 36.6 204.7 130.0 165.8 6 ”.2 45.7 210.7 130.5 165.0 7 88.5 55.0 218.5 130.0 164.6 8 87.5 62.1 226.7 131.2 166.6 8 103.7 68.3 234.4 130.7 165.1 10 Finish 110.2 ' 76.8 241.2 131.0 164.3 11 120.0 ”.2 250.0 130.0 164.6 12 127.2 82.5 257.3 130.1 164.8 13 134.7 100.4 268.5 131.8 166.1 14 142.6 113.5 274.0 131.4 165.5 15 148.8 115.4 281.1 131.2 165.7 16 158.8 123.6 280.0 131 .1 166.5 17 167.5 132.7 297.8 130.4 165.1 71 18 174.8 138.6 305.3 130.4 165.7 18 182.8 147.6 313.3 130.5 165.7 20 181.3 155.8 322.3 131.0 186.5 21 188.4 163.1 328.5 130.1 166.5 22 205.8 170.8 338.7 132.8 167.8 23 215.8 180.2 346.6 130.8 188.4 24 223.8 188.7 355.1 131.2 166.4 25 230.5 185.7 383.3 132.8 187.6 26 238.5 206.0 372.3 132.8 166.3 27 246.7 211.7 380.1 133.4 168.4 28 869. 6681 m 255.5 220.5 388.2 133.7 168.7 28 265.4 228.4 388.0 133.5 168.5 30 273.0 238.0 405.8 132.8 167.8 31 280.5 246.8 414.8 134.3 187.8 32 281.3 258.5 425.2 1 33.8 1 68.7 33 300.5 264.1 433.4 133.0 168.3 34 307.7 273.1 440.8 133.2 187.7 35 317.3 281.3 450.6 133.3 1 68.3 36 326.1 280.6 460.5 1 34.4 168.8 37 335.8 288.8 468.3 133.6 168.4 38 346.2 308.5 478.8 133.7 170.4 38 353.8 317.6 487.4 133.5 168.8 40 383.2 328.5 486.7 133.5 170.2 41 373.1 335.6 506.1 133.0 170.5 42 3&3 344.8 515.5 1 34.6 170.7 43 380.8 353.4 525.4 134.5 171.8 44 400.0 362.4 534.3 134.3 171.8 45 407.2 370.7 542.4 135.3 171 .7 46 418.3 381.1 553.2 134.8 172.2 47 427.0 380.3 5&.8 136.8 1 73.6 48 435.8 386.7 571 .5 135.8 172.8 48 444.7 407.3 5&8 1 38.1 173.5 50 452.1 416.3 588.7 136.6 1 72.4 51 4&.0 424.2 587.8 134.8 173.7 52 470.8 432.8 806.8 136.0 174.0 53 4&.3 442.8 618.5 1 36.2 173.8 54 4&.7 448.6 824.2 134.8 1 74.6 55 4&.4 458.0 &2.8 1 34.5 1 74.8 56 505.0 465.8 840.8 135.8 174.8 57 514.2 474.0 648.8 135.6 175.7 58 521.8 482.4 657.1 135.1 174.7 58 528.4 481 .3 888.3 1 36.8 175.0 60 538.1 487.1 673.2 137.1 178.1 61 543.2 508.2 882.5 138.3 178.3 82 550.0 512.0 888.2 138.2 177.2 & 557.7 518.4 887.3 138.8 177.8 84 584.8 525.5 703.2 1 38.3 177.7 85 572.4 533.4 711.8 138.4 178.4 88 081011 577.4 538.8 71 6.0 1 38.6 176.2 72 67 586.4 546.5 725.0 138.6 178.5 88 582.1 553.6 731.3 138.1 177.7 68 587.8 558.8 738.0 140.1 178.1 70 603.5 565.1 743.4 138.8 178.3 71 611.4 571.8 750.5 138.1 178.7 72 61 7.1 576.4 754.8 137.8 178.5 73 624.3 582.7 783.1 138.8 180.4 74 628.4 588.6 788.7 140.3 180.1 75 833.4 584.7 774.7 141.3 180.0 76 840.8 801.3 763.0 142.2 181.7 M8! 142.2 181.7 Min 128.4 164.3 Dlfl -13.8 -17.4 APPENDIX D Calculations of y axis movements of the Mobile Video Platform 73 Framo(0.01 Ts) Event Y(itfrtcam)(cm) Y(rttrtcamXcm) ‘ 45.3 45.1 46.4 46.5 45.6 45.4 46.2 46.1 47.1 46.4 46.0 45.5 DCNOG.UN ......aa-na OG‘UN-‘O 22 23 24 25 26 27 28 28 30 888218888169: 3: Flnlsh random 78) Y(mamXcm) Y(rflrtcam )(om) d 46.6 42.7 46.1 44.1 45.2 46.6 45.6 44.7 45.6 43.5 44.6 44.0 46.5 44.4 46.2 44.7 46.6 44.2 44.6 44.6 46.7 44.7 46.4 46.0 46.6 44.6 46.4 45.1 2 6 4 5 6 7 6 6 d“““ “Chan-0° 44.6 45.6 46.0 45.7 45.3 45.0 44.7 44.0 46.5 44.5 44.6 809 Sat Nov! 53 54 55 56 57 56 56 60 885882882 ‘4“ ‘0 C anqom Ts) Evan! Y(ltfrtcamXcm) Y(tflflcamXcm) ‘ 41 .6 42.6 40.6 42.2 42.0 42.5 42.6 42.7 42.4 43.3 43.0 43.6 OONOO‘UN ‘-“d‘ O‘cflMdO 20 21 22 23 24 25 26 27 a 26 30 88:88“ ‘ S C an0(0.0178) Y(ItmcamXcm) Y(rtfncamXcm) ‘ 41 .6 42.6 40.6 42.2 42.0 42.5 42.6 42.7 42.4 43.3 43.0 43.6 OOQOC‘IUN ‘fi‘fid ‘UN‘O 20 21 22 23 24 25 26 27 26 26 N a g 8883886882 a ‘ 62 63 64 65 66 67 66 66 70 mmqom 7s) Y(mmamXcm) Y(mmXcln) 40.2 36.2 40.1 37.4 36.6 36.7 36.6 36.2 36.7 36.3 36.1 36.3 .CQOG‘HN-fi ....Aaaa- 00.063-50 888388683 6882 53 54 55 56 57 56 56 60 O . APPENDIX E Qalculations of z m‘s movements of the Mobile Video Platform 80 Z-axis movements(cm) Trial 1 :1qu F anowm 78 Event Z(lflneam) Z(rmtum) Z(shell) cum") (lawman) MW!!!) «mm 1 216.6 516.1 365.2 2 217.1 520.4 365.7 0.5 0.6 2.3 2.6 3 220.2 521 .7 365.3 -0.4 3.0 1 .3 4.4 4 21 6.2 5&5 366.4 1.2 .1 .0 0.6 -0.2 5 222.5 525.4 360.5 4.1 3.4 2.6 6.3 6 223.4 526.7 366.7 -0.6 0.6 1 .4 2.2 7 223.3 526.6 360.3 0.7 -0.1 0.1 0.0 6 225.7 “.3 361 .5 1.2 2.5 1.5 4.0 6 224.6 527.6 3&3 -0.6 -0.6 -0.4 .1 .2 10 CM 226.6 531.2 ”4.3 3.4 2.0 3.3 5.2 1 1 220.2 530.4 ”.1 .1 .2 1 .3 -0.6 0.5 12 ”6.0 526.5 363.6 0.5 -0.2 0.6 -1.0 1 3 226.3 530.6 364.6 1 .2 0.3 1 .3 1 .7 14 226.6 534.5 367.5 2.7 1.5 3.6 5.1 1 5 232.1 535.3 366.5 -1 .0 2.3 0.6 3.1 16 232.5 536.6 367.1 0.6 0.4 1 .5 1 .6 17 230.5 533.1 366.1 -1.0 -2.0 3.7 -5.7 16 231 .5 536.6 330.2 2.1 1.0 3.6 4.6 16 232.6 536.6 366.0 0.6 1.3 -0.2 1.1 an 234.1 537.2 “.0 1.0 1.3 0.4 1.6 21 234.7 536.6 400.6 0.7 0.6 2.7 3.3 22 235.6 540.2 401.2 0.6 1.1 0.3 1.4 23 236.7 642.6 “.6 -0.4 0.6 2.4 3.2 24 236.3 544.1 403.1 2.4 2.6 1.4 4.1 25 240.0 544.0 403.1 0.0 0.7 4,1 0.6 26 236.3 544.1 402.7 -0.5 -1 .6 0.2 -1 .6 27 236.6 544.1 402.5 -0.1 1.3 .o_1 1.2 26 240.4 546.4 403.6 1.0 0.6 2.3 3.1 26 240.6 546.2 403.4 -0.2 0.3 «0.2 0.0 30 243.7 646.6 404.7 1.3 3.1 2.6 6.7 31 244.2 551.5 404.7 0.0 0.5 2.6 3.2 m 62 DIM 244.6 646.1 04.6 -0.1 0.4 -2.6 4.1 33 244.2 646.4 404.4 -0.2 -0.6 0.4 0.0 34 240.2 560.6 406.6 2.4 1.6 1.6 3.5 a 246.0 662.7 «.1 1.3 1.6 1.7 3.6 8 250.5 555.0 “.7 0.6 2.4 2.4 4.6 37 246.6 555.1 «.1 -0.6 -0.6 0.1 «0.6 36 252.6 555.7 410.0 1.6 3.1 0.6 3.7 36 251.1 656.5 “.6 -1.4 -1.6 0.6 4.1 Q 251 .7 556.6 406.6 1.2 0.6 0.4 1.1 41 253.1 556.6 410.1 0.3 1.4 2.0 3.4 42 254.0 557.6 4M6 o1.5 0.6 -1.3 -0.4 43 253.0 556.6 410.0 1.5 -1.0 1.4 0.3 44 256.3 561.0 412.3 2.3 3.3 2.0 5.4 45 256.1 561.6 412.3 «0.1 -0.2 0.6 0.6 46 255.5 562.2 41 1.0 -1 .3 -0.6 0.4 -0.2 81 47 255.6 562.9 409.6 ~1.2 0.1 0.7 0.6 46 256.0 563.3 411.6 2.0 2.4 0.4 2.6 49 256.6 564.7 411 .2 -0.6 0.6 1.4 2.0 50 256.1 564.9 413.3 2.0 -0.5 0.2 «0.3 51 256.3 565.0 414.6 1.5 1.2 0.1 1.3 52 260.5 564.5 413.4 -1 .4 1 .1 -0.4 0.7 53 261.4 566.4 413.5 0.1 1.0 1.6 2.6 54 F1111.“ 260.6 566.6 413.9 0.4 -0.7 0.2 -0.4 55 261.2 567.3 413.6 -0.2 0.5 0.7 1 .2 56 262.1 567.9 414.0 0.4 0.9 0.6 1 .6 57 260.7 566.7 412.2 -1.6 -1.5 -1 .2 -2.7 56 261.6 567.7 413.5 1.2 1.1 1.0 2.1 59 261.0 566.0 413.3 -0.1 -0.6 0.3 -0.5 60 262.5 566.6 413.4 0.1 1 .6 1 .6 3.2 61 263.6 566.1 413.6 0.4 1 .3 -0.5 0.7 62 264.2 571 .4 41 3.6 0.0 0.4 2.3 2.6 '6! 6.3 Ila -6.7 W 1 1 .9 Taxis movements(cm) Trial 2 mum-m Ffllllqo.“ 76 5V6!“ 2011mm) Z(M) 21611611) 521“” WI!) MN) MW”) 1 -62.6 212.6 61 .6 2 “.3 212.3 59.2 -2.4 -3.6 -0.3 4.6 3 -62.1 21 6.1 61 .6 2.6 4.3 3.6 6.1 4 -63.6 214.0 61 .2 -0.6 01 .5 -2.1 -3.6 5 -61 .6 21 5.6 61 .6 0.4 1 .6 1 .6 3.2 6 -64.6 21 3.3 56.0 -3.6 -2.7 -2.3 -5.0 7 -62.2 21 5.7 62.6 4.6 2.5 2.5 4.6 6 “.6 214.2 61 .2 -1 .4 1 .6 -1 .5 0.0 6 -61 .4 21 5.6 61 .6 0.4 ‘0.6 1 .6 0.6 10 ”111611 -63.6 215.6 60.6 -0.7 -2.5 0.0 -2.5 1 1 -61 .2 21 5.3 ”.6 -0.3 2.6 -0.5 2.3 12 -64.7 216.2 56.1 ~2.5 4.5 -2.1 -5.7 1 3 -61 .7 214.6 61 .0 2.6 3.0 1 .6 4.6 14 “.6 21 6.2 ' 61 .6 1 .0 0.6 1 .4 2.3 15 “.6 21 7.3 62.6 0.6 2.0 1 .1 3.1 16 -63.2 213.3 56.3 4.5 -4.4 -4.1 -6.5 17 -61 .7 21 6.2 61 .6 2.6 1 .6 2.6 4.5 1 6 «I61 .1 21 5.0 61 .2 -0.7 0.6 -1 .2 -0.6 16 -62.6 215.1 61 .6 0.6 -1.5 0.0 -1.5 20 -62.6 212.6 56.6 -1 .6 40.2 -2.2 -2.4 21 -62.0 214.1 61 .4 1 .5 0.6 1 .2 2.0 22 -61.6 215.1 61.6 0.4 0.1 1.0 1.1 23 “.2 217.3 61.6 0.0 1.6 2.2 3.9 24 -62.6 21 2.7 60.1 -1 .7 -2.7 -4.6 ~7.3 25 -61 .7 216.7 63.6 3.2 1.3 6.0 7.3 26 “.6 21 6.6 62.5 -0.6 1 .1 -2.1 -1 .0 82 27 -60.6 215.6 63.4 0.6 -0.2 «0.7 -0.6 26 -66.7 216.7 64.0 0.5 1.1 0.6 1.6 26 -60.5 216.2 62.4 -1.6 «0.6 -0.5 o1.4 m 30 Nov! -60.3 216.4 63.3 1.0 0.2 0.3 0.4 31 -60.3 217.2 64.3 1.0 0.1 0.6 0.6 32 -60.0 217.1 62.7 -1.6 0.3 -0.1 0.1 33 *3 21 6.0 63.6 1 .1 1.7 -1.1 0.6 34 -60.6 216.4 64.5 0.7 -2.3 3.4 1 .1 35 «67 .7 21 6.6 63.6 -0.6 2.6 0.2 3.1 36 “.5 216.1 63.5 -0.4 -0.6 .1 .5 -2.3 37 -66.6 217.2 65.2 1 .7 -0.3 -0.6 -1.2 36 -66.6 21 6.5 65.3 0.1 -0.1 -0.7 -0.6 36 -66.0 21 6.1 65.6 0.6 «0.1 1.6 1.5 40 «67 .6 21 6.6 64.6 -1.3 1.1 1.7 2.6 41 *1 21 6.6 65.6 1 .3 -0.7 «0.2 -0.6 42 -66.6 220.1 66.5 0.7 1 .6 0.5 2.2 43 «C3 21 6.7 67.6 1 .3 .1 .4 -0.4 .1 .7 44 -65.1 220.2 66.5 0.7 3.2 0.5 3.7 45 «64.5 221 .1 66.0 -0.5 0.7 0.6 1.5 46 «67 .6 21 6.7 67.7 -0.3 -3.5 -2.4 -5.6 47 “.4 220.3 66.6 1 .0 1 .5 1 .6 3.2 46 -64.1 221 .6 66.6 -2.0 2.3 1 .3 3.5 46 -64.7 m .6 71.3 4.5 -0.5 0.2 -0.3 50 -64.2 216.6 66.0 -2.4 0.4 -2.0 -1 .6 51 -62.5 £35 76.6 7.6 1 .7 3.7 5.5 52 42.5 221 .5 71 .4 -5.2 -0.3 -2.0 -2.3 53 “.6 ”5.2 75.6 4.4 2.0 3.7 5.7 54 -61 .3 224.1 71 .5 -4.2 -0.5 -1 .1 .1 .6 55 -62.6 224.3 73.6 2.3 -1 .6 0.2 -1 .4 56 «61 .3 224.6 71 .6 -2.0 1 .7 0.5 2.1 57 “.7 226.7 76.7 4.6 0.6 1 .6 2.5 55 -61 .0 25.1 74.6 -1 .6 «0.3 -1 .6 -1 .6 an “.2 an: 76.3 4.5 0.7 1 .6 2.5 60 -76.4 227.2 75.1 -4.2 1 .6 0.2 2.1 61 -76.3 221.: 76.1 1 .0 0.1 0.6 0.6 62 076.6 227.7 76.2 0.1 .1 .3 -0.3 .1 .6 63 “.7 227.4 75.5 «0.6 -1 .2 -0.3 -1 .4 64 -76.7 226.0 76.6 1 .3 4.0 1 .6 5.5 65 -76.6 as 77.5 0.7 0.0 -0.5 -0.5 66 m -76.1 m 75.5 -2.1 ~23 -1 .6 4.6 67 -76.4 231 .0 76.1 3.6 2.7 4.2 6.6 66 ~77.4 231.0 76.3 0.2 -1.0 -0.1 -1.1 66 -76.2 226.6 61 .0 1.7 1.2 -1.2 0.0 70 -75.5 231 .4 76.3 -2.7 0.7 1 .7 2.4 71 «74.6 ”6.6 ”.3 2.0 0.7 -1 .6 -0.6 72 -75.4 233.2 ”.2 0.0 -0.5 3.3 2.6 73 -74.1 232.0 ”.7 0.5 1 .2 -1 .2 0.1 74 -73.6 232.0 ”.0 -0.7 0.6 0.1 0.6 75 -75.6 231 .6 76.5 «0.5 -2.2 «0.3 -2.5 83 Max 6 1 I I Mln 43.5 I Diff 1 6.6 Calculation of Luis movements(cm) Trial 5 | witmeem )tl Freme(0.01Te Event Z(ltmeern) Z(rtmcem) Z(shell) dztshell) dzm‘tfrtcem) durtmeem) 02011110601) — 1 210.5 51 6.6 362.6 2 213.7 516.6 365.6 2.7 3.2 2.7 5.6 3 216.2 521.7 365.6 0.0 2.4 2.1 4.5 4 216.0 524.0 367.6 2.3 2.6 2.4 5.2 5 221.7 526.6 400.6 2.7 2.6 4.5 7.2 6 223.3 526.0 400.3 -0.3 1.6 0.4 2.0 7 226.2 531 .2 402.4 2.0 3.0 2.2 5.2 6 227.1 532.6 403.6 1 .2 0.6 1.4 2.3 6 226.3 534.3 “.1 1 .5 1.2 1 .7 2.6 10 Catch 226.6 536.0 406.0 0.6 1.3 1.7 3.0 11 233.2 536.1 407.7 1.7 3.6 3.1 6.7 12 232.7 540.0 “.5 0.6 -0.4 0.6 0.4 13 234.1 541.1 410.0 1.5 1.4 1.2 2.6 14 235.4 542.0 410.6 0.6 1 .2 0.6 2.1 15 237.5 543.4 412.2 1.3 2.2 1.4 3.5 16 236.1 547.5 41 5.1 2.6 1.6 4.1 5.7 17 236.7 547.1 414.1 -1.0 -0.4 -0.4 «0.6 1 6 241.0 546.6 417.2 3.1 2.4 1.7 4.1 16 240.0 546.1 414.6 -2.3 -1.0 -0.7 -1 .6 20 243.5 550.4 416.7 1 .6 3.5 2.3 5.6 21 243.6 551 .6 416.2 1 .5 0.2 1 .5 1 .7 22 245.7 555.0 41 6.2 1.0 2.1 3.0 5.1 23 246.7 554.6 416.3 0.1 1.1 «0.4 0.6 24 247.2 555.6 420.4 1.2 0.5 1 .1 1 .5 25 251.3 556.2 421.3 0.6 4.1 2.5 6.6 26 250.4 556.6 421.4 0.1 -0.6 0.5 -0.4 27 253.1 562.4 423.6 2.4 2.7 3.6 6.6 26 253.2 562.5 424.6 1 .1 0.1 0.0 0.1 a 253.6 563.4 424.6 0.0 0.7 0.6 1.6 so 255.: 5a.: 425.: 0.7 1.5 m u 31 255.2 566.6 426.7 1.2 -0.1 2.5 2.4 32 256.6 567.4 427.0 0.2 1.7 1.7 3.4 33 257.2 566.0 427.6 0.6 0.2 0.6 0.6 34 256.3 570.3 426.4 0.7 2.1 2.2 4.3 35 261 .2 572.3 430.3 1 .6 1 .6 2.0 4.0 mm 36 Dflve 263.6 573.6 431 .3 1.0 2.4 1 .3 3.7 37 264.0 575.1 431 .5 0.2 0.4 1 .6 2.0 36 267.1 575.7 431.4 -0.1 3.1 0.6 3.7 36 265.6 577.0 432.6 1.4 -1 .2 1 .3 0.1 40 265.6 576.3 432.5 -0.4 0.0 -0.6 -0.6 41 266.6 576.6 433.7 1.2 3.0 3.5 6.5 42 271.0 562.7 436.6 3.2 2.1 2.6 5.0 43 271 .2 562.2 434.6 -2.1 0.2 -0.5 -0.3 84 44 272.4 562.0 436.2 1.4 1.2 -0.2 0.9 45 274.5 565.7 437.9 1.6 2.1 3.7 5.6 46 274.2 566.2 436.6 0.6 -0.3 0.5 0.1 47 276.3 566.6 436.3 «0.3 2.1 0.7 2.6 46 277.1 567.1 436.5 0.2 0.6 0.2 1.0 46 276.6 667.6 436.3 «0.2 «0.3 0.6 0.5 50 260.7 591.5 440.0 1.7 3.6 3.5 7.4 61 261.0 563.1 440.4 0.4 0.4 1.7 2.0 52 276.3 561 .2 436.1 -2.2 -1 .7 -1 .6 4.7 53 263.6 566.0 443.4 5.2 4.5 4.6 6.3 64 261 .6 564.6 441 .5 -1 .6 .1 .6 -1 .2 3.1 55 264.6 566.6 443.4 1 .6 3.0 1.6 4.6 56 266.0 566.0 443.7 0.3 1 .1 1 .2 2.3 57 ”5.7 567.4 443.5 -0.2 «0.3 «0.6 «0.6 56 265.5 5N4 442.3 -1.2 -0.2 1.0 0.6 56 “.0 666.6 444.7 2.4 0.5 1 .6 1 .6 60 Flnlsh 266.2 601 .6 443.4 -1 .3 0.2 1 .6 2.1 61 267.2 601 .5 444.6 1 .5 1.0 -0.3 0.7 62 266.1 604.1 443.6 -1 .3 0.6 2.7 3.6 63 266.6 604.0 443.7 0.1 1.5 -0.1 1 .4 64 260.1 604.0 443.6 -0.1 0.4 0.0 0.4 66 266.3 604.5 443.0 -0.6 -0.6 0.5 0.3 66 267.6 603.1 442.0 -1.0 -1.4 .1 .4 -2.6 67 261.5 606.0 442.6 0.6 3.6 2.6 6.5 66 266.1 605.0 441.6 -0.6 -2.4 -1.0 3.4 66 261.1 606.6 441.6 0.2 2.0 1.6 3.6 70 266.6 605.2 443.3 1 .3 .1 .5 -1 .7 3.2 flex 6.3 “In -3.7 0111 12.6 Calculation of Luis movements(cm) Trial 6 damn ‘anqom Te Event Z(Mbern) Z(rflrtoeln) Z(ehell) damn) 621M) MM) ammo-m) 1 56.1 356.0 an 2 56.6 367.3 226.2 0.4 0.6 2.4 3.2 3 60.6 366.1 231.0 1 .7 2.1 0.6 2.6 4 63.0 360.5 232.3 1.3 2.1 2.4 4.4 5 62.6 361 .6 232.3 0.0 «0.2 1 .1 1.0 6 62.3 361 .2 231 .7 06 -0.6 -0.4 -1.0 7 66.3 ”6.4 233.7 2.1 4.1 4.1 5.2 6 66.0 366.6 236.6 1.7 2.6 1.5 4.1 6 66.6 366.6 236.1 0.7 1.0 2.7 3.7 1 0 Finish 70.6 370.2 235.6 -0.2 1 .0 0.7 1.7 11 73.2 372.2 237.7 1.6 2.3 2.0 4.2 12 74.6 373.7 236.4 1.7 1 .3 1.5 2.6 1 3 75.0 375.5 241.6 2.1 0.6 1.6 2.3 14 76.2 376.5 241.5 0.0 1 .2 0.6 2.2 15 76.1 377.3 243.2 1.7 1 .6 0.6 2.7 16 76.4 376.5 243.6 0.7 1.3 2.2 3.5 85 17 60.2 376.5 244.6 1.0 0.6 0.0 0.6 16 62.6 361.6 245.2 0.4 2.4 2.3 4.7 16 62.2 363.7 246.6 1 .6 -0.4 1.6 1.6 20 63.0 364.1 247.5 0.6 0.6 0.4 1.2 21 64.2 364.5 246.5 -0.6 1.2 0.4 1.6 22 65.0 366.5 246.4 2.6 0.6 1.6 2.6 23 67.3 356.5 246.4 -0.1 2.3 0.1 2.4 24 66.7 360.6 246.6 0.6 2.4 4.0 6.4 25 66.5 360.2 250.4 0.5 -1.2 «0.3 -1 .6 26 60.6 362.2 251.2 0.6 2.1 2.0 4.1 27 66.7 362.6 251.0 -0.1 -0.6 0.6 «0.3 26 61.0 365.6 253.6 2.5 1.3 2.6 4.2 26 62.3 363.1 251.2 -2.4 1.2 -2.6 -1.3 30 62.0 364.1 251.6 0.7 -0.2 1.0 0.6 31 63.6 367.1 255.4 3.5 1.5 3.0 4.6 32 66.7 366.3 256.6 1.4 3.2 2.1 5.3 33 ”.5 ”.2 255.6 .1 .0 1.6 .1 .1 0.7 34 66.4 401 .5 254.6 .1 .1 -0.2 3.3 3.2 35 100.2 401 .6 255.6 1.2 1.6 0.1 1.6 36 66.5 403.7 257.7 1.6 «0.6 2.1 1.5 37 100.3 403.3 256.6 -0.6 0.6 -0.4 0.4 36 102.6 405.2 256.1 1.2 2.5 1 .6 4.4 36 103.5 405.3 260.2 2.1 0.6 0.1 0.7 40 104.3 406.3 256.3 -0.6 0.6 1.0 1.6 41 104.5 “.3 260.3 1 .0 0.3 2.1 2.4 42 104.3 407.6 260.2 -0.1 «0.3 «0.4 -0.7 43 1 04.6 “.2 260.0 -0.3 0.6 0.3 0.6 44 106.3 410.0 260.0 0.1 1 .4 1 .6 3.2 45 106.6 410.2 56.6 -0.3 0.3 0.2 0.5 46 105.6 412.4 262.6 2.6 -0.6 2.2 1.4 47 107.2 41 1.5 261 .3 -1.2 1 .4 -0.6 0.6 46 1 “.6 412.6 262.6 1.2 1.3 1.3 2.6 46 110.5 413.6 262.6 0.2 1.6 1.1 3.0 50 107.3 414.4 261 .3 -1 .5 -3.2 0.5 -2.7 51 1 10.1 415.0 26444 3.1 2.6 0.6 3.5 52 1N2 414.3 261.5 -2.6 -2.0 -0.7 -2.7 53 11 0.0 416.1 263.1 1.6 1.6 1.6 3.6 54 1 1 0.2 41 6.5 261 .6 -1 .3 0.2 0.4 0.5 55 1 1 1 .1 41 6.2 262.6 1 .0 0.6 -0.3 0.6 66 1 06.4 416.0 261 .6 «0.6 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I l l Bold values were the values used as the movement of the MVP. l Bigitizing error Trial 1 X(lfeainLen) Y(IfealnLen) Z(lfcamLen) "1:0an X(rteamLen) Y(rteamLen) Z(MmLen) rte-mun icmi (cm) (on) (on) (cm) (on) (on) ion) Maximum 17.: 0.5 5.1 17.0 19.4 0.0 52 10.0 [Mnirnun 14.0 .0.: .1.0 14.7 15.4 -0.1 -2.1 10.5 IDlflerence 3.2 0.9 0.1 3.1 3.0 0.9 7.3 3.1 | Trial 2 [Maxim-n 31.9 0.7 7.0 32.5 20.0 0.7 4.0 21.2 |Miniumm 14.4 .02 4.7 14.5 15.0 4.1 4.4 10.0 IDiflerence 17.5 0.0 12.5 10.1 3.0 0.0 7.5 4.3 | Trial 5 |Maximim 10.5 0.0 5.0 24.: 21.7 0.8 0.3 22.2 IMnimun 14.4 .0.: -1.2 15.4 16.8 -0.2 4.9 15.0 |oinmnce 4.2 0.0 5.2 7.9 4.0 1.0 7.1 5.4 | Trial 6 |Maxmn 10.0 0.7 4.0 25.3 20.3 1.0 5.9 20.5 Minimum 14.0 0.1 4.0 17.0 10.0 0.1 4.0 17.0 IDlfl‘erence 4.7 0.0 5.0 7.4 3.5 0.9 8.0 3.5 Movements of the MVP in th—e—Y'i plane Triall Y(fm- m0- Archn Y(bk)‘ 20*)- Arolln «mm 21mm mwzim» mum-mi make-m» mama» Y(rlMcem) Zimmm) Y(rtbkoem) Z(rtbkcem) (OM) in) (mi (mi 1cm) (door-u) Maximum 45.7 401.5 17.4 1.3 400.2 0.0 Minimum 40.2 407.7 15.0 4.4 400.0 4.2 Differenc 0.5 5.2 1.5 4.7 0.0 0.0 Trial 2 | _M_aximum1 45.5 404.0 17.1 2.4 404.2 0.2 | Minimum] 44.1 410.4 15.0 .1.1 411.4 -0.4 I Differenc 7.7 0.4 1.3 3.5 7.2 0.5 Trial 5 | Maximum 43.0 405.0 15.2 0.5 402.0 04 | Minimum 41.4 415.0 15.2 4.3 415.5 4.1 Difierenc 0.5 11.0 1.0 4.0 12.7 0.9 ‘T'riai 5 | _M_aximum .77.5 .2003 17.5 4.2 403.4 0.0 | Minimum 40.: 410.1 14.0 4.2 410.7 4.5 Differenc 10.3 13.2 2.9 4.5 17.2 0.0 1 18 respect to -axis movement 17.4 cm -axis movement 16.6 cm f MVP to camera = 128.3 cm a change of 16.6 cm changes to 1 1.8cm -axis movement 8.9 Trial Xm- vim- Arne-n X00- Vim- mun Xmas-m» warm-m» mnvximi Armani Y(Wml- mnvxmi X(ltbkcem) Y(ltbkcem) degrees X(rbkeern) Y(rbkeern) degreee (cm) (cm) (door-u) ion) (an) (deems) 17.0 0.0 2.2 10.4 0.0 2.5 14.5 4.3 .1.0 10.4 -0.1 4.4 Differenc 3.2 0.0 3.2 3.0 0.0 3.0 Trial 2 0.7 2.3 200 0.7 2.2 4.0 10.0 -0.1 -0.3 0.0 3.0 3.0 0.0 2.5 Trial 5 52.5 21.7 0.0 2.2 40.5 10.0 -0.2 -0.7 Differenc . 2.0 4.0 1.0 2.0 1.0 3.0 0.1 0.3 Differenc . 0.0 2.7 rial 1 nah-air mimo- ximo-mi wane-mi (cm) (on) 133.3 105.0 127.2 101.0 Differenc 4.1 4.0 2 140.2 155.2 135.2 157.3 Differenc -5.0 -7.0 178.0 182.0 Differenc -14.0 181.7 164.3 Differenc - 119 1 Y(lttrtcem) Y(rtfrtcam) (en) (cm) 47.4 40.0 42.7 43.0 Differenc 4.7 5.1 rial 2 47.0 47.4 43.0 42.7 3.0 4.0 5 45.4 40.0 Differenc 4.7 T 5 40.4 Differenc 0.5 Differenc Differenc Differenc Differenc APPENDIX J Digitized Coordinates, do! and do; / dQ calculations of Point A 120 121 00.0 00.0 00.0 :0 05,0 5N,0 00.0 :0 00.0 000 N00 5.5 ,:2~N_>0Q .um 0N0. 00,0 00 w .0>( 0.0. 0,55 0,0. 0.0. 0.05 m 5. 0 F. 0 05 0 N... 0.0. 0.55 €05. 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E. ..N n .2..... u» ..5 Q... n .228 .x ”.2..: ..v , 143 o. 252. APPENDIX N Digitized Coordinates, d_n,; and dQ,; / dQ calculations of Point E 144 145 146 147 148 o. 2:2”. m 0E2”. 2 .59... m 0E8. m .52“. v .82”. . .EE. N ..5... 149 APPENDIX 0 Digitized Coordinates, dni and dn! / dQ calculations of Point F 150 151 152 153 154 155 APPENDIX P Digitized Coordinates, d_n,; and dn_, / dQ calculations of Point G 156 157 158 159 160 161 APPENDIX Q Digitized Coordinates, dn, and dn, / dQ calculations of Point H 162 163 164 165 166 167 LIST OF REFERENCES LIST OF REFERENCES Ariel, Gideon (1993). Age] Perform;ance Am System (APAS) User’s Manual. San Diego, Ariel Life Systems, Inc. Blatt, F.J.(1986). Princrp' les of Emcs (2nd ed.). Massachusetts: Allyn & Bacon. Boland, A.L., Hosea, T.M.(l991). Rowing and Sculling and the Older Athlete, Clinics in Sports Medicine, 10, 245-256. Celentano, F., Cortili, G., Prampero, P.E., Cerretelli, P.(l97l). Mechanical aspects of rowing, Journal of Applied Employ, 36, 642—647. Challis, J.H., Kerwin, D.G. (1992). Accuracy Assessment and Control Point Configuration When Using the DLT for Photogrammetery. Journal of Biomechanics, 25, 1053-1058. Challis, J .H.(1995). A Multiphase Cah‘bration Procedure for the Direct Linear Transformation, Journal of Applied Biomechanicg 11, 351-358. Holden, D.L. , Jackson, D.W.(l985). Stress fracture of the ribs in female rowers, AmerimJoumal of Sm Medicine, 13, 342-347. Hosea, T.M., Boland, A.L., McCarthy, K., Kennedy, T.(l989). Rowing Injuries, Postgraduate Advances in Sm Medicine, 1-15. Hosea, T. , Boland, A.L., Simon, S.R., Pasciotta, J. McCarthy, K. (1987). Myoelectric and Kinematic Analysis of the Lumbar Spine while Rowing, American Journal of Sm Medicine, 15, Abstract. Howell, D.W.(l984). Musculoskeletal profile and incidence of musculoskeletal injuries in lightweight women rowers, American Journal of Sm Medicine, 12, 278-282. Lamb, D.PL(1989). A kinematic comparison of ergometer and on-water rowing. 'I_'h£ American Journal of Sufi Medicine, 17, 367-373. Martin, T.P., Bemfield, J.S.(1980). Eifect of stroke rate on velocity of a rowing shell, Medicine and Science in 8293 and Exercise, 12, 250-256. 168 169 Martindale, W.O., Robertson, D.G. E. (1984). Mechanical Energy in Sculling and in Rowing an Ergometer, Canadian Journal of Applied Sport Sciences. 9, 153-163. Munro, A.R.( 1979). Some Basic Biomechanics of Rowing, Sports Coach, 3(4), 3-5. Nelson, W.N., Mdule, C.J.(1983). Kinematic analysis and efficiency estimate of intercollegiate female rowers, Medicine and Science in Sports and Exercis_§_, 1 5, 535- 541. Pannell, W.J.(l979). Mechanics of Oar, Boat and Body. Sports Coach, 3(4), 14-20. Schneider, 13., Angst, F., Brandt, J.D.(l978). Biomechanics in rowing, Biomechanics VI-B, 115-119. ' Shapiro, R(197 8). Direct Linear Transformation Method for Three-Dimensional Cinematography, The Research (gum, 49, 197-205. Winter, D.A.(1990). Biomechanics and Motor Con_trol of Human Movement (2nd ed.). New York: John Wiley & Sons. Illllllllllllllll